Podcasts about Mathematics

In this episode of the Crazy Wisdom Podcast, host Stewart Alsop interviews Aurelio Gialluca, an economist and full stack data professional who works across finance, retail, and AI as both a data engineer and machine learning developer, while also exploring human consciousness and psychology. Their wide-ranging conversation covers the intersection of science and psychology, the unique cultural characteristics that make Argentina a haven for eccentrics (drawing parallels to the United States), and how Argentine culture has produced globally influential figures from Borges to Maradona to Che Guevara. They explore the current AI landscape as a "centralizing force" creating cultural homogenization (particularly evident in LinkedIn's cookie-cutter content), discuss the potential futures of AI development from dystopian surveillance states to anarchic chaos, and examine how Argentina's emotionally mature, non-linear communication style might offer insights for navigating technological change. The conversation concludes with Gialluca describing his ambitious project to build a custom water-cooled workstation with industrial-grade processors for his quantitative hedge fund, highlighting the practical challenges of heat management and the recent tripling of RAM prices due to market consolidation.Timestams00:00 Exploring the Intersection of Psychology and Science02:55 Cultural Eccentricity: Argentina vs. the United States05:36 The Influence of Religion on National Identity08:50 The Unique Argentine Cultural Landscape11:49 Soft Power and Cultural Influence14:48 Political Figures and Their Cultural Impact17:50 The Role of Sports in Shaping National Identity20:49 The Evolution of Argentine Music and Subcultures23:41 AI and the Future of Cultural Dynamics26:47 Navigating the Chaos of AI in Culture33:50 Equilibrating Society for a Sustainable Future35:10 The Patchwork Age: Decentralization and Society35:56 The Impact of AI on Human Connection38:06 Individualism vs. Collective Rules in Society39:26 The Future of AI and Global Regulations40:16 Biotechnology: The Next Frontier42:19 Building a Personal AI Lab45:51 Tiers of AI Labs: From Personal to Industrial48:35 Mathematics and AI: The Foundation of Innovation52:12 Stochastic Models and Predictive Analytics55:47 Building a Supercomputer: Hardware InsightsKey Insights1. Argentina's Cultural Exceptionalism and Emotional Maturity: Argentina stands out globally for allowing eccentrics to flourish and having a non-linear communication style that Gialluca describes as "non-monotonous systems." Argentines can joke profoundly and be eccentric while simultaneously being completely organized and straightforward, demonstrating high emotional intelligence and maturity that comes from their unique cultural blend of European romanticism and Latino lightheartedness.2. Argentina as an Underrecognized Cultural Superpower: Despite being introverted about their achievements, Argentina produces an enormous amount of global culture through music, literature, and iconic figures like Borges, Maradona, Messi, and Che Guevara. These cultural exports have shaped entire generations worldwide, with Argentina "stealing the thunder" from other nations and creating lasting soft power influence that people don't fully recognize as Argentine.3. AI's Cultural Impact Follows Oscillating Patterns: Culture operates as a dynamic system that oscillates between centralization and decentralization like a sine wave. AI currently represents a massive centralizing force, as seen in LinkedIn's homogenized content, but this will inevitably trigger a decentralization phase. The speed of this cultural transformation has accelerated dramatically, with changes that once took generations now happening in years.4. The Coming Bifurcation of AI Futures: Gialluca identifies two extreme possible endpoints for AI development: complete centralized control (the "Mordor" scenario with total surveillance) or complete chaos where everyone has access to dangerous capabilities like creating weapons or viruses. Finding a middle path between these extremes is essential for society's survival, requiring careful equilibrium between accessibility and safety.5. Individual AI Labs Are Becoming Democratically Accessible: Gialluca outlines a tier system for AI capabilities, where individuals can now build "tier one" labs capable of fine-tuning models and processing massive datasets for tens of thousands of dollars. This democratization means that capabilities once requiring teams of PhD scientists can now be achieved by dedicated individuals, fundamentally changing the landscape of AI development and access.6. Hardware Constraints Are the New Limiting Factor: While AI capabilities are rapidly advancing, practical implementation is increasingly constrained by hardware availability and cost. RAM prices have tripled in recent months, and the challenge of managing enormous heat output from powerful processors requires sophisticated cooling systems. These physical limitations are becoming the primary bottleneck for individual AI development.7. Data Quality Over Quantity Is the Critical Challenge: The main bottleneck for AI advancement is no longer energy or GPUs, but high-quality data for training. Early data labeling efforts produced poor results because labelers lacked domain expertise. The future lies in reinforcement learning (RL) environments where AI systems can generate their own high-quality training data, representing a fundamental shift in how AI systems learn and develop.

https://www.youtube.com/watch?v=shwbIXkaZPs Podcast audio: This talk comparing Newton and Descartes approach to mathematics by David Bakker was recorded live on July 2nd in Boston, MA as part of the 2025 Objectivist Summer Conference and is available on the Ayn Rand Institute Podcast stream. Listen and subscribe wherever you get your podcasts. Watch archived podcasts here. Image Credits: Newton: GeorgiosArt / iStock / via Getty Images. Descartes: ilbusca / DigitalVision Vectors / via Getty Images

Ever notice that it's not the everyday conversations or simple disagreements that shape the quality of a relationship—it's those high-stakes moments, the tough talks that feel risky and uncomfortable, that truly define the connection. Far too often, we skirt around what really needs to be said, trading short-term relief for long-term regret. Whether it's at work or at home, these avoided discussions can lead to resentment, disconnection, and a sense of self-abandonment. In this episode, listeners will dive deep into understanding why we tend to avoid these "last 8%" conversations, what emotional forces are at play, and how learning emotional intelligence can transform conflict into an opportunity for growth. Through practical insights and relatable stories, the discussion explores how you can recognize your own patterns under pressure, build self-awareness, and learn strategies to approach difficult dialogues with clarity, empathy, and courage. If you're ready to break out of avoidance and start showing up authentically—for yourself and your relationships—this episode offers a roadmap to addressing the hard stuff and reclaiming connection. Bill Benjamin is a Partner at the Institute for Health & Human Potential. He has degrees in Mathematics and Computer Science and 30 years of business experience. Bill explains how you can build a high-performance Last 8% Culture by leveraging the science of emotional intelligence. His clients include NASA, Marriott, Intel, the Mayo Clinic, the U.S. Marines and Surgeons.   Episode Highlights 05:07 The importance and science behind emotional intelligence in relationships and business. 07:24 The origin of the "Last 8%" concept and its impact on difficult conversations. 10:03 Fight, flight, and the roles we play: Avoiders, mess-makers, and emotional triggers in relationships. 14:39 Navigating emotional intelligence at work versus at home. 18:16 The costs of avoidance. 21:06 Recognizing your role and contribution in conflict. 28:36 Understanding others' intentions in pressure situations. 29:15 Practical strategies for handling relational conflict. 35:12 Addressing shame and trauma in relationship pressure points. 36:15 Taking action: Sensitive communication and resources for emotional intelligence development.   Your Check List of Actions to Take Start with Self-Awareness: Regularly check in with your body and mind for early signs of emotional activation, like tense muscles or scattered thoughts. Pause Before Reacting: If you notice emotional triggers, pause and take several deep breaths to regain mental clarity and composure. Name Your Patterns: Reflect on whether you tend to avoid difficult conversations or "make a mess" by confronting too strongly. Get Curious About Others: In moments of tension, intentionally seek to understand the other person's perspective—what's driving their reaction or behavior? Build Empathy Bridges: Imagine stepping over to the "other side of the bridge," as suggested, to genuinely validate the other person's feelings before expressing your own. Return To The Conversation: If you need a break during a heated moment, communicate that you'll revisit the topic, rather than letting it drop indefinitely. Express Your Emotional Needs: Practice communicating your own needs and boundaries directly, knowing it's essential for building mutual respect and trust. Seek Support When Needed: If shame, trauma, or persistent avoidance is hindering healthy interactions, reach out to a therapist, mentor, or supportive resource for guidance and perspective.   Mentioned Performing Under Pressure: The Science of Doing Your Best When It Matters Most (*Amazon Affiliate link) (book) The Secret to Building a High-Performing Team (Harvard Business Review article) 12 Relationship Principles to Strengthen Your Love (free guide) Connect with Bill Benjamin Websites: ihhp.com Facebook: facebook.com/IHHPGlobal X: x.com/IHHP YouTube: youtube.com/channel/UC0UYI0Vuy99P8Hdj-r3hr4w Instagram: instagram.com/ihhpglobal LinkedIn: linkedin.com/in/bill-benjamin-12b671  

Episode: 1500 1500th episode and 2000 AD: A poor time to summarize.  Today, we reach a landmark.

One winter morning, listener Jane opened her curtains to find her car roof covered in breathtaking, fern-like frost so intricate it looked like a William Morris print. But how does something as ordinary as ice create patterns so beautifully complex?Hannah and Dara explore this crunchy, slippery, delicately patterned branch of chemistry to uncover the rules and mysteries that govern the extra-ordinary world of ice. Why does ice come in so many shapes and sizes? And does all ice form at 0 degrees Celsius? Is every snowflake truly unique? We have questions a plenty for our eager chemists, who, as all good chemists do, have a few demonstrations up their sleeves to help explain. And we explore nature's hidden geometry to find why these frost ferns follow the same rules as lightning bolts, river deltas and even human lungs. You can send your everyday mysteries for the team to investigate to: curiouscases@bbc.co.ukContributors Sarah Hart – Professor Emerita of Mathematics, Birkbeck University of London Christoph Salzmann – Professor of Physical and Materials Chemistry, UCL Dr Thomas Whale – Lecturer, Institute for Climate and Atmospheric Science, University of LeedsProducer: Emily Bird Executive Producer: Sasha Feachem A BBC Studios Production

Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he’s the #1 highest-rated user on MathOverflow. He is also the author of several books, including Proof and the Art of Mathematics and Lectures on the Philosophy of Mathematics. And he has a great blog called Infinitely More. Thank you for listening ❤ Check out our sponsors: https://lexfridman.com/sponsors/ep488-sc See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. Transcript: https://lexfridman.com/joel-david-hamkins-transcript CONTACT LEX: Feedback – give feedback to Lex: https://lexfridman.com/survey AMA – submit questions, videos or call-in: https://lexfridman.com/ama Hiring – join our team: https://lexfridman.com/hiring Other – other ways to get in touch: https://lexfridman.com/contact EPISODE LINKS: Joel’s X: https://x.com/JDHamkins Joel’s Website: https://jdh.hamkins.org Joel’s Substack: https://www.infinitelymore.xyz Joel’s MathOverflow: https://mathoverflow.net/users/1946/joel-david-hamkins Joel’s Papers: https://jdh.hamkins.org/publications Joel’s Books: Lectures on the Philosophy of Mathematics: https://amzn.to/3MThaAt Proof and the Art of Mathematics: https://amzn.to/3YACc9A SPONSORS: To support this podcast, check out our sponsors & get discounts: Perplexity: AI-powered answer engine. Go to https://www.perplexity.ai/ Fin: AI agent for customer service. Go to https://fin.ai/lex Miro: Online collaborative whiteboard platform. Go to https://miro.com/ CodeRabbit: AI-powered code reviews. Go to https://coderabbit.ai/lex Chevron: Reliable energy for data centers. Go to https://chevron.com/power Shopify: Sell stuff online. Go to https://shopify.com/lex LMNT: Zero-sugar electrolyte drink mix. Go to https://drinkLMNT.com/lex MasterClass: Online classes from world-class experts. Go to https://masterclass.com/lexpod OUTLINE: (00:00) – Introduction (01:58) – Sponsors, Comments, and Reflections (15:40) – Infinity & paradoxes (1:02:50) – Russell’s paradox (1:15:57) – Gödel’s incompleteness theorems (1:33:28) – Truth vs proof (1:44:52) – The Halting Problem (2:00:45) – Does infinity exist? (2:18:19) – MathOverflow (2:22:12) – The Continuum Hypothesis (2:31:58) – Hardest problems in mathematics (2:41:25) – Mathematical multiverse (3:00:18) – Surreal numbers (3:10:55) – Conway’s Game of Life (3:13:11) – Computability theory (3:23:04) – P vs NP (3:26:21) – Greatest mathematicians in history (3:40:05) – Infinite chess (3:58:24) – Most beautiful idea in mathematics

Support the show to get full episodes, full archive, and join the Discord community. The Transmitter is an online publication that aims to deliver useful information, insights and tools to build bridges across neuroscience and advance research. Visit thetransmitter.org to explore the latest neuroscience news and perspectives, written by journalists and scientists. Read more about our partnership. Sign up for Brain Inspired email alerts to be notified every time a new Brain Inspired episode is released. To explore more neuroscience news and perspectives, visit thetransmitter.org. Alex is an associate professor of psychology at Vanderbilt University where he heads the Maier Lab. His work in neuroscience spans vision, visual perception, and cognition, studying the neurophysiology of cortical columns, and other related topics. Today, he is here to discuss where his focus has shifted over the past few years, the neuroscience of consciousness. I should say shifted back, since that was his original love, which you'll hear about. I've known Alex since my own time at Vanderbilt, where I was a postdoc and he was a new faculty member, and I remember being impressed with him then. I was at a talk he gave - job talk or early talk - where it was immediately obvious how passionate and articulate he is about what he does, and I remember he even showed off some of his telescope photography - good pictures of the moon, I remember. Anyway, we always had fun interactions, even if sometimes it was a quick hello as he ran up stairs and down hallways to get wherever he was going, always in a hurry. Today we discuss why Alex sees integration information theory as the most viable current prospect for explaining consciousness. That is mainly because IIT has developed a formalized mathematical account that hopes to do for consciousness what other math has done for physics, that is, give us what we know as laws of nature. So basically our discussion revolves around everything related to that, like philosophy of science, distinguishing mathematics from "the mathematical", some of the tools he is finding valuable, like category theory, and some of his work measuring the level of consciousness IIT says a whole soccer team has, not just the individuals that comprise the team. Maier Lab Astonishing Hypothesis (Alex's youtube channel) Twitter: Sensation and Perception textbook (in-the-making) Related papers Linking the Structure of Neuronal Mechanisms to the Structure of Qualia Information integration and the latent consciousness of human groups Neural mechanisms of predictive processing: a collaborative community experiment through the OpenScope program Various things Alex mentioned: “An Antiphilosophy of Mathematics,” Peter J. Freyd youtube video about "the mathematical". David Kaiser's playlist on modern physics. 0:00 - Intro 4:27 - Discovering consciousness science 11:23 - Laws of perception 15:48 - Integrated information theory and mathematical formalism 23:54 - Theories of consciousness without math 28:18 - Computation metaphor 34:44 - Formalized mathematics is the way 36:56 - Category theory 41:42 - Structuralism 51:09 - The mathematical 54:33 - Metaphysics of the mathematical 59:52 - Yoneda Lemma 1:12:05 - What's real 1:26:22 - Measuring consciousness of a soccer team 1:35:03 - Assumptions and approximations of IIT 1:43:13 - Open science

Pada episode ini kita rangkum capaian matematika dan bahasan matematika ter-hot di tahun ini.Bahasan utama mulai dari (1:26:30)

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This is a special episode, highlighting a session from ELC Annual 2025! OpenAI evolved from a pure research lab into the fastest-growing product in history, scaling from 100 million to 700 million weekly users in record time. In this episode, we deconstruct the organizational design choices and cultural bets that enabled this unprecedented velocity. We explore what it means to hire "extreme generalists," how AI-native interns are redefining productivity, and the real-time trade-offs made during the world's largest product launches. Featuring Sulman Choudhry (Head of ChatGPT Engineering) and Samir Ahmed (Technical Lead), moderated by Lawrence Bruhmeller (Eng Management @ Sigma). ABOUT SULMAN CHOUDHRYSulman leads ChatGPT Engineering at OpenAI, driving the development and scaling of one of the world's most impactful AI products. He pushes the boundaries of innovation by turning cutting‑edge research into practical, accessible tools that transform how people interact with technology. Previously at Meta, Sulman founded and scaled Instagram Reels, IGTV, and Instagram Labs, and helped lead the early development of Instagram Stories.He also brought MetaAI to Instagram and Messenger, integrating generative AI into experiences used by billions. Earlier in his career, Sulman was on the founding team that built and launched UberEATS from the ground up, helping turn it into a global food delivery platform. With a track record of marrying technical vision, product strategy, and large‑scale execution, Sulman focuses on building products that meaningfully change how people live, work, and connect.ABOUT SAMIR AHMEDSamir is the Technical Lead for ChatGPT at OpenAI, where he currently leads the Personalization and Memory efforts to scale adaptive, useful, and human-centered product experiences to over 700 million users. He works broadly across the OpenAI stack—including mobile, web, services, systems, inference, and product research infrastructure.Previously, Samir spent nine years at Snap, working across Ads, AR, Content, and Growth. He led some of the company's most critical technical initiatives, including founding and scaling the machine learning platform that powered nearly all Ads, Content, and AR workloads, handling tens of billions of requests and trillions of inferences daily.ABOUT LAWRENCE BRUHMELLERLawrence Bruhmuller has over 20 years of experience in engineering management, much of it as an overall head of engineering. Previous roles include CTO/VPE roles at Great Expectations, Pave, Optimizely, and WeWork. He is currently leading the core query compiler and serving teams at Sigma Computing, the industry leading business analytics company.Lawrence is passionate about the intersection of engineering management and the growth stage of startups. He has written extensively on engineering leadership (https://lbruhmuller.medium.com/), including how to best evolve and mature engineering organizations before, during and after these growth phases. He enjoys advising and mentoring other engineering leaders in his spare time.Lawrence holds a Bachelors and Masters in Mathematics and Engineering from Harvey Mudd College. He lives in Oakland, California, with his wife and their three daughters. This episode is brought to you by Span!Span is the AI-native developer intelligence platform bringing clarity to engineering organizations with a holistic, human-centered approach to developer productivity.If you want a complete picture of your engineering impact and health, drive high performance, and make smarter business decisions…Go to Span.app to learn more! SHOW NOTES:From research lab to record-breaking product: Navigating the fastest growth in history (4:03)Unpredictable scaling: Handling growth spurts of one million users every hour (5:20)Cross-stack collaboration: How Android, systems, and GPU engineers solve crises together (7:06)The magic of trade-offs: Aligning the team on outcomes like service uptime vs. broad availability (7:57)Why throwing models "over the wall" failed and how OpenAI structures virtual teams (11:17)Lessons from OpenAI's first intern class: Why AI-native new grads are crushing expectations (13:41)Non-hierarchical culture: Using the "Member of Technical Staff" title to blur the lines of expertise (15:37)AI-native engineering: When massive code generation starts breaking traditional CI/CD systems (16:21)Asynchronous workflows: Using coding agents to reduce two-hour investigations to 15 minutes (17:35)The mindset shift: How rapid model improvements changed how leaders audit and trust code (19:00)Predicting success: "Vibes-based" decision making and iterative low-key research previews (20:43)Hiring for high variance: Why unconventional backgrounds lead to high-potential engineering hires (22:09) LINKS AND RESOURCESLink to the video for this sessionLink to all ELC Annual 2025 sessions This episode wouldn't have been possible without the help of our incredible production team:Patrick Gallagher - Producer & Co-HostJerry Li - Co-HostNoah Olberding - Associate Producer, Audio & Video Editor https://www.linkedin.com/in/noah-olberding/Dan Overheim - Audio Engineer, Dan's also an avid 3D printer - https://www.bnd3d.com/Ellie Coggins Angus - Copywriter, Check out her other work at https://elliecoggins.com/about/ Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Are quantum computers an existential threat to Bitcoin, or is the fear mostly FUD?In this episode, Bartosz Naskręcki, Vice-Dean of Mathematics and Computer Science at Adam Mickiewicz University, breaks down how Bitcoin's cryptography actually works, the math behind SHA-256, why SHA-1 failed, and what quantum computing can and cannot realistically do to Bitcoin today — or the foreseeable future.---00:00 – Introduction and Episode Overview02:30 – What Hash Functions Are and Why They Matter06:39 – The Avalanche Effect Explained12:09 – Why Bitcoin Uses SHA-25619:48 – Why GitHub Still Uses SHA-125:46 – How SHA-256 Improved on SHA-134:54 – Quantum Computing Breakthroughs and Bitcoin Security49:09 – What Quantum Computers Actually Are---

The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability (Bloomsbury, 2025) is an open access book that covers four decades of work by the leading Australian philosopher, mathematician and historian of ideas, James Franklin.These interlinking essays are connected by a core theme: the necessary structures in reality that allow certain knowledge of absolute truths. Franklin's Aristotelian realist philosophy of mathematics shows how mathematical truths are directly about physical reality, and at the same time certainly and provably true. Ranging from mathematics to evidence evaluation to ethics, his philosophy of probability sees the relation of evidence to hypothesis, such as in science and law, as purely logical, hence necessary.Across ethics and the philosophy of religion, the theme of necessity is repeated: basic ethical truths (such as the worth of persons and the wrongness of murder) are shown to have the same certainty as mathematics. Focus on the history of ideas connects the philosophical work in the present with the medieval scholastic tradition, which defended similar necessities but is now neglected.Here is an up-to-date introduction to Franklin's overall perspective. Recalling Western philosophy to its roots, it reveals the way absolute necessities are discoverable across the abstract fields of mathematics, logical evidence and ethics. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/new-books-network

Learning to teach math teachers better as we share our keynote, Learning as a Mathematics Teacher Educator, from the 2025 AMTE Virtual Institute, themed Across the Arc: Sustaining Our Learning, Sharing Our Practice.

The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability (Bloomsbury, 2025) is an open access book that covers four decades of work by the leading Australian philosopher, mathematician and historian of ideas, James Franklin.These interlinking essays are connected by a core theme: the necessary structures in reality that allow certain knowledge of absolute truths. Franklin's Aristotelian realist philosophy of mathematics shows how mathematical truths are directly about physical reality, and at the same time certainly and provably true. Ranging from mathematics to evidence evaluation to ethics, his philosophy of probability sees the relation of evidence to hypothesis, such as in science and law, as purely logical, hence necessary.Across ethics and the philosophy of religion, the theme of necessity is repeated: basic ethical truths (such as the worth of persons and the wrongness of murder) are shown to have the same certainty as mathematics. Focus on the history of ideas connects the philosophical work in the present with the medieval scholastic tradition, which defended similar necessities but is now neglected.Here is an up-to-date introduction to Franklin's overall perspective. Recalling Western philosophy to its roots, it reveals the way absolute necessities are discoverable across the abstract fields of mathematics, logical evidence and ethics. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/science

1144. This week, we look at the origin of the letter X as the variable for the unknown in algebra. Then, we look at the phrase "how come," explaining why it's more informal than "why" and how its grammar subtly differs from other question words.That X segment was written by Peter Schumer, Professor of Mathematics and Natural Philosophy at Middlebury College, and it originally appeared on The Conversation and appears here through a Creative Commons license.Links to Get One Month Free of the Grammar Girl Patreon (different links for different levels)Order of the Snail ($1/month level): https://www.patreon.com/grammargirl/redeem/687E4Order of the Aardvark ($5/month level): https://www.patreon.com/grammargirl/redeem/07205Keeper of the Commas ($10/month level): https://www.patreon.com/grammargirl/redeem/50A0BGuardian of the Grammary ($25/month level): https://www.patreon.com/grammargirl/redeem/949F7

The Artifact Research Foundation conducts archaeological, metrological, and historical research to explore the technological capabilities of prehistoric human cultures.​Human evolution is long and mysterious.  Today, we know very little about our ancient ancestors, save for stories passed down through time.  Physical remains of archaic human civilization may seem elusive, yet modern forensic methods can uncover more than we ever thought possible.​We approach forensic archaeology from a multi-disciplinary perspective.  The world's biggest story is also the world's biggest mystery.  To unlock it requires a different approach.  Our researchers come from diverse fields such as Mathematics, Physics, Engineering, Manufacturing, Geology, Computer Science, History, Art, and Literature.Adam YoungFounder and ResearcherAdam is an independent researcher with a background in mathematical statistics. Over the past decade, he has researched ancient artifacts throughout the world, most notably in Egypt. He was the first researcher to apply modern Metrology to analyze predynastic stone vessels in a controlled setting. With the help of other dedicated professionals, he founded the Artifact Research Foundation to study advanced machining in ancient Egypt and elsewhere. Members of the foundation have diverse backgrounds, but are united in a common purpose:  to analyze, document, and publish results to help further our understanding of ancient cultures.https://www.artifactfoundation.org/Become a supporter of this podcast: https://www.spreaker.com/podcast/earth-ancients--2790919/support.

Indigenous math isn't just about numbers and equations, it involves culture, spirituality and more. Math professor Edward Doolittle, a Mohawk from Six Nations in Ontario, sees math as something embedded in Creation itself. In his Hagey Lecture at the University of Waterloo, he describes Indigenous mathematics as being grounded in cognition, emotion, the physical world and community. Indigenizing math, Doolittle hopes, will make it more approachable and meaningful to Indigenous students — show them how entwined it is with everyday life and something much bigger than ourselves.

Janet Walkoe & Margaret Walton, Exploring the Seeds of Algebraic Reasoning ROUNDING UP: SEASON 4 | EPISODE 8 Algebraic reasoning is defined as the ability to use symbols, variables, and mathematical operations to represent and solve problems. This type of reasoning is crucial for a range of disciplines.  In this episode, we're talking with Janet Walkoe and Margaret Walton about the seeds of algebraic reasoning found in our students' lived experiences and the ways we can draw on them to support student learning.  BIOGRAPHIES Margaret Walton joined Towson University's Department of Mathematics in 2024. She teaches mathematics methods courses to undergraduate preservice teachers and courses about teacher professional development to education graduate students. Her research interests include teacher educator learning and professional development, teacher learning and professional development, and facilitator and teacher noticing. Janet Walkoe is an associate professor in the College of Education at the University of Maryland. Janet's research interests include teacher noticing and teacher responsiveness in the mathematics classroom. She is interested in how teachers attend to and make sense of student thinking and other student resources, including but not limited to student dispositions and students' ways of communicating mathematics. RESOURCES "Seeds of Algebraic Thinking: a Knowledge in Pieces Perspective on the Development of Algebraic Thinking" "Seeds of Algebraic Thinking: Towards a Research Agenda" NOTICE Lab  "Leveraging Early Algebraic Experiences"  TRANSCRIPT Mike Wallus: Hello, Janet and Margaret, thank you so much for joining us. I'm really excited to talk with you both about the seeds of algebraic thinking. Janet Walkoe: Thanks for having us. We're excited to be here.  Margaret Walton: Yeah, thanks so much. Mike: So for listeners, without prayer knowledge, I'm wondering how you would describe the seeds of algebraic thinking. Janet: OK. For a little context, more than a decade ago, my good friend and colleague, [Mariana] Levin—she's at Western Michigan University—she and I used to talk about all of the algebraic thinking we saw our children doing when they were toddlers—this is maybe 10 or more years ago—in their play, and just watching them act in the world. And we started keeping a list of these things we saw. And it grew and grew, and finally we decided to write about this in our 2020 FLM article ["Seeds of Algebraic Thinking: Towards a Research Agenda" in For the Learning of Mathematics] that introduced the seeds of algebraic thinking idea. Since they were still toddlers, they weren't actually expressing full algebraic conceptions, but they were displaying bits of algebraic thinking that we called "seeds." And so this idea, these small conceptual resources, grows out of the knowledge and pieces perspective on learning that came out of Berkeley in the nineties, led by Andy diSessa. And generally that's the perspective that knowledge is made up of small cognitive bits rather than larger concepts. So if we're thinking of addition, rather than thinking of it as leveled, maybe at the first level there's knowing how to count and add two groups of numbers. And then maybe at another level we add two negative numbers, and then at another level we could add positives and negatives. So that might be a stage-based way of thinking about it.  And instead, if we think about this in terms of little bits of resources that students bring, the idea of combining bunches of things—the idea of like entities or nonlike entities, opposites, positives and negatives, the idea of opposites canceling—all those kinds of things and other such resources to think about addition. It's that perspective that we're going with. And it's not like we master one level and move on to the next. It's more that these pieces are here, available to us. We come to a situation with these resources and call upon them and connect them as it comes up in the context. Mike: I think that feels really intuitive, particularly for anyone who's taught young children. That really brings me back to the days when I was teaching kindergartners and first graders.  I want to ask you about something else. You all mentioned several things like this notion of "do, undo" or "closing in" or the idea of "in-betweenness" while we were preparing for this interview. And I'm wondering if you could describe what these things mean in some detail for our audience, and then maybe connect them back with this notion of the seeds of algebraic thinking. Margaret: Yeah, sure. So we would say that these are different seeds of algebraic thinking that kids might activate as they learn math and then also learn more formal algebra. So the first seed, the doing and undoing that you mentioned, is really completing some sort of action or process and then reversing it.  So an example might be when a toddler stacks blocks or cups. I have lots of nieces and nephews or friends' kids who I've seen do this often—all the time, really—when they'll maybe make towers of blocks, stack them up one by one and then sort of unstack them, right? So later this experience might apply to learning about functions, for example, as students plug in values as inputs, that's kind of the doing part, but also solve functions at certain outputs to find the input. So that's kind of one example there.  And then you also talked about closing in and in-betweenness, which might both be related to intervals. So closing in is a seed where it's sort of related to getting closer and closer to a desired value. And then in formal algebra, and maybe math leading up to formal algebra, the seed might be activated when students work with inequalities maybe, or maybe ordering fractions.  And then the last seed that you mentioned there, in-betweenness, is the idea of being between two things. For example, kids might have experiences with the story of Goldilocks and the Three Bears, and the porridge being too hot, too cold, or just right. So that "just right" is in-between. So these seats might relate to inequalities and the idea that solutions of math problems might be a range of values and not just one. Mike: So part of what's so exciting about this conversation is that the seeds of algebraic thinking really can emerge from children's lived experience, meaning kids are coming with informal prior knowledge that we can access. And I'm wondering if you can describe some examples of children's play, or even everyday tasks, that cultivate these seeds of algebraic thinking. Janet: That's great. So when I think back to the early days when we were thinking about these ideas, one example stands out in my head. I was going to the grocery store with my daughter who was about three at the time, and she just did not like the grocery store at all. And when we were in the car, I told her, "Oh, don't worry, we're just going in for a short bit of time, just a second." And she sat in the back and said, "Oh, like the capital letter A." I remember being blown away thinking about all that came together for her to think about that image, just the relationship between time and distance, the amount of time highlighting the instantaneous nature of the time we'd actually be in the store, all kinds of things.  And I think in terms of play examples, there were so many. When she was little, she was gifted a play doctor kit. So it was a plastic kit that had a stethoscope and a blood pressure monitor, all these old-school tools. And she would play doctor with her stuffed animals. And she knew that any one of her stuffed animals could be the patient, but it probably wouldn't be a cup. So she had this idea that these could be candidates for patients, and it was this—but only certain things. We refer to this concept as "replacement," and it's this idea that you can replace whatever this blank box is with any number of things, but maybe those things are limited and maybe that idea comes into play when thinking about variables in formal algebra. Margaret: A couple of other examples just from the seeds that you asked about in the previous question. One might be if you're talking about closing in, games like when kids play things like "you're getting warmer" or "you're getting colder" when they're trying to find a hidden object or you're closing in when tuning an instrument, maybe like a guitar or a violin.  And then for in-betweeness, we talked about Goldilocks, but it could be something as simple as, "I'm sitting in between my two parents" or measuring different heights and there's someone who's very tall and someone who's very short, but then there are a bunch of people who also fall in between. So those are some other examples. Mike: You're making me wonder about some of these ideas, these concepts, these habits of mind that these seeds grow into during children's elementary learning experiences. Can we talk about that a bit? Janet: Sure. Thank you for that question.  So we think of seeds as a little more general. So rather than a particular seed growing into something or being destined for something, it's more that a seed becomes activated more in a particular context and connections with other seeds get strengthened. So for example, the idea of like or nonlike terms with the positive and negative numbers. Like or nonlike or opposites can come up in so many different contexts. And that's one seed that gets evoked when thinking potentially when thinking about addition. So rather than a seed being planted and growing into things, it's more like there are these seeds, these resources that children collect as they act on the world and experience things. And in particular contexts, certain seeds are evoked and then connected. And then in other contexts, as the context becomes more familiar, maybe they're evoked more often and connected more strongly. And then that becomes something that's connected with that context. And that's how we see children learning as they become more expert in a particular context or situation. Mike: So in some ways it feels almost more like a neural network of sorts. Like the more that these connections are activated, the stronger the connection becomes. Is that a better analogy than this notion of seeds growing? It's more so that there are connections that are made and deepened, for lack of a better way of saying it? Janet: Mm-hmm. And pruned in certain circumstances. We actually struggled a bit with the name because we thought seeds might evoke this, "Here's a seed, it's this particular seed, it grows into this particular concept." But then we really struggled with other neurons of algebraic thinking. So we tossed around some other potential ideas in it to kind of evoke that image a little better. But yes, that's exactly how I would think about it. Mike: I mean, just to digress a little bit, I think it's an interesting question for you all as you're trying to describe this relationship, because in some respects it does resemble seeds—meaning that the beginnings of this set of ideas are coming out of lived experiences that children have early in their lives. And then those things are connected and deepened—or, as you said, pruned. So it kind of has features of this notion of a seed, but it also has features of a network that is interconnected, which I suspect is probably why it's fairly hard to name that. Janet: Mm-hmm. And it does have—so if you look at, for example, the replacement seed, my daughter playing doctor with her stuffed animals, the replacement seed there. But you can imagine that that seed, it's domain agnostic, so it can come out in grammar. For instance, the ad-libs, a noun goes here, and so it can be any different noun. It's the same idea, different context. And you can see the thread among contexts, even though it's not meaning the same thing or not used in the same way necessarily. Mike: It strikes me that understanding the seeds of algebraic thinking is really a powerful tool for educators. They could, for example, use it as a lens when they're planning instruction or interpreting student reasoning. Can you talk about this, Margaret and Janet? Margaret: Yeah, sure, definitely. So we've seen that teachers who take a seeds lens can be really curious about where student ideas come from. So, for example, when a student talks about a math solution, maybe instead of judging whether the answer is right or wrong, a teacher might actually be more curious about how the student came to that idea. In some of our work, we've seen teachers who have a seeds perspective can look for pieces of a student answer that are productive instead of taking an entire answer as right or wrong. So we think that seeds can really help educators intentionally look for student assets and off of them. And for us, that's students' informal and lived experiences. Janet: And kind of going along with that, one of the things we really emphasize in our methods courses, and is emphasized in teacher education in general, is this idea of excavating for student ideas and looking at what's good about what the student says and reframing what a student says, not as a misconception, but reframing it as what's positive about this idea. And we think that having this mindset will help teachers do that. Just knowing that these are things students bring to the situation, these potentially productive resources they have. Is it productive in this case? Maybe. If it's not, what could make it more productive? So having teachers look for these kinds of things we found as helpful in classrooms. Mike: I'm going to ask a question right now that I think is perhaps a little bit challenging, but I suspect it might be what people who are listening are wondering, which is: Are there any generalizable instructional moves that might support formal or informal algebraic thinking that you'd like to see elementary teachers integrate into their classroom practice? Margaret: Yeah, I mean, I think, honestly, it's: Listen carefully to kids' ideas with an open mind. So as you listen to what kids are saying, really thinking about why they're saying what they're saying, maybe where that thinking comes from and how you can leverage it in productive ways. Mike: So I want to go back to the analogy of seeds. And I also want to think about this knowing what you said earlier about the fact that some of the analogy about seeds coming early in a child's life or emerging from their lived experiences, that's an important part of thinking about it. But there's also this notion that time and experiences allow some connections to be made and to grow or to be pruned.  What I'm thinking about is the gardener. The challenge in education is that the gardener who is working with students in the form of the teacher and they do some cultivation, they might not necessarily be able to kind of see the horizon, see where some of this is going, see what's happening. So if we have a gardener who's cultivating or drawing on some of the seeds of algebraic thinking in their early childhood students and their elementary students, what do you think the impact of trying to draw on the seeds or make those connections can be for children and students in the long run? Janet: I think [there are] a couple of important points there. And first, one is early on in a child's life. Because experiences breed seeds or because seeds come out of experiences, the more experiences children can have, the better. So for example, if you're in early grades, and you can read a book to a child, they can listen to it, but what else can they do? They could maybe play with toys and act it out. If there's an activity in the book, they could pretend or really do the activity. Maybe it's baking something or maybe it's playing a game. And I think this is advocated in literature on play and early childhood experiences, including Montessori experiences. But the more and varied experiences children can have, the more seeds they'll gain in different experiences.  And one thing a teacher can do early on and throughout is look at connections. Look at, "Oh, we did this thing here. Where might it come out here?" If a teacher can identify an important seed, for instance, they can work to strengthen it in different contexts as well. So giving children experiences and then looking for ways to strengthen key ideas through experiences. Mike: One of the challenges of hosting a podcast is that we've got about 20 to 25 minutes to discuss some really big ideas and some powerful practices. And this is one of those times where I really feel that. And I'm wondering, if we have listeners who wanted to continue learning about the ways that they can cultivate the seeds of algebraic thinking, are there particular resources or bodies of research that you would recommend? Janet: So from our particular lab we have a website, and it's notice-lab.com, and that's continuing to be built out. The project is funded by NSF [the National Science Foundation], and we're continuing to add resources. We have links to articles. We have links to ways teachers and parents can use seeds. We have links to professional development for teachers. And those will keep getting built out over time.  Margaret, do you want to talk about the article? Margaret: Sure, yeah. Janet and I actually just had an article recently come out in Mathematics Teacher: Learning and Teaching from NCTM [National Council of Teachers of Mathematics]. And it's [in] Issue 5, and it's called "Leveraging Early Algebraic Experiences." So that's definitely another place to check out.  And Janet, anything else you want to mention? Janet: I think the website has a lot of resources as well. Mike: So I've read the article and I would encourage anyone to take a look at it. We'll add a link to the article and also a link to the website in the show notes for people who are listening who want to check those things out.  I think this is probably a great place to stop. But I want to thank you both so much for joining us. Janet and Margaret, it's really been a pleasure talking with both of you. Janet: Thank you so much, Mike. It's been a pleasure.  Margaret: You too. Thanks so much for having us. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2025 The Math Learning Center | www.mathlearningcenter.org  

Jim Elvidge is an independent researcher and author whose work challenges conventional cosmology by proposing that the universe itself may be a computational system. In The Universe — Solved, Elvidge presents a bold framework suggesting that reality is not fundamentally physical, but information-based, governed by mathematical rules similar to those underlying digital computation. Drawing on concepts from physics, information theory, and philosophy, he explores how space, time, energy, and consciousness may emerge from a deeper informational substrate. Elvidge's ideas invite a radical rethinking of existence—one that blurs the line between science and metaphysics and raises profound questions about the nature of reality and humanity's place within it.Become a supporter of this podcast: https://www.spreaker.com/podcast/the-x-zone-radio-tv-show--1078348/support.Please note that all XZBN radio and/or television shows are Copyright © REL-MAR McConnell Meda Company, Niagara, Ontario, Canada – www.rel-mar.com. For more Episodes of this show and all shows produced, broadcasted and syndicated from REL-MAR McConell Media Company and The 'X' Zone Broadcast Network and the 'X' Zone TV Channell, visit www.xzbn.net. For programming, distribution, and syndication inquiries, email programming@xzbn.net.We are proud to announce the we have launched TWATNews.com, launched in August 2025.TWATNews.com is an independent online news platform dedicated to uncovering the truth about Donald Trump and his ongoing influence in politics, business, and society. Unlike mainstream outlets that often sanitize, soften, or ignore stories that challenge Trump and his allies, TWATNews digs deeper to deliver hard-hitting articles, investigative features, and sharp commentary that mainstream media won't touch.These are stories and articles that you will not read anywhere else.Our mission is simple: to expose corruption, lies, and authoritarian tendencies while giving voice to the perspectives and evidence that are often marginalized or buried by corporate-controlled media

This episode of Room to Grow, Curtis and Joanie reflect back on 2025 and all that they learned during the year. A significant number of 2025 episodes of Room to Grow were focused on the Mathematics Teaching Practices from NCTM's Principles to Actions, celebrating the 10th anniversary of its publication. Curtis and Joanie highlighted how these practices have survived the test of time, and continue to reflect good teaching in mathematics. Additionally, our hosts preview what new topics they are hoping to learn and explore podcast episodes about in 2026.  Additional referenced content includes:·       NTCM's Principles to Actions and Taking Action books·       Pam Harris' website and book·       Julianne Foxworthy Gonzalez, Ph.D. in Mathematics Education. Math guidelines for supporting multi-language learners (MLLs). All of us at Room to Grow wish you a peaceful holiday season! Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.   

In the 1800s, it seemed like mathematics was a solved problem. The paradoxes in the field were resolved, and even areas like advanced calculus could be taught consistently and reliably at any school. It was clearly understandable in a way that abstract fields like philosophy weren’t, and it was on its way to solving humanity’s problems. Mathematical work on electromagnetism made modern electrical engineering and power systems possible. New research in algebra created the logical basis for future computer science and digital circuits. But then new problems appeared. In the early 20th century, mathematicians made discoveries that showed them enough to know how little they really knew. Bertrand Russell showed that at its edges, math fell apart. It couldn’t fully define itself on its own terms without becoming logically inconsistent. He gave the analogy of a small-town barber who shaves everyone who doesn't shave himself; the question is, who shaves the barber—if he shaves himself, he breaks the rule, but if he doesn't shave himself, he must, by the rule, shave himself? In today’s episode, I’m speaking to Jason Bardi, author of The Great Math War: How Three Brilliant Minds Fought for the Foundations of Mathematics and we explore the story of three competing efforts by mathematicians to resolve this crisis. What do you do if math, the most logical of all sciences, becomes illogical at a certain point? Bertrand Russell thought the problem could be solved with even more logic, we just hadn’t tried hard enough. David Hilbert thought redemption lay in accepting mathematics as a formal game of arbitrary rules, no different from the moves and pieces in chess. And L. E. J. Brouwer argued math is entirely rooted in human intuition—and that math is not based on logic but rather logic is based on math. Set against the backdrop of one of the most turbulent periods of European history (from the late 19th century through World War I, the 1920s, the Great Depression, and the early days of World War II), we look at what happens when rock-solid truths don’t seem so rock solid anymore.See omnystudio.com/listener for privacy information.

SummaryIn this episode, Shannon Valenzuela and Peter Ulrickson explore the significance of the Quadrivium in education and Dr. Ulrickson's unique presentation of teaching these arts in his books A Brief Quadrivium and the accompanying teacher's guide. They discuss the interconnectedness of mathematics and the arts and highlight the unique perspectives offered by each discipline. They explore the importance of modeling, proof, and observation and the role of rhetoric and logic in mathematics. The conversation also addresses the sensory engagement in learning and the value of teaching mathematics classically.Topics Covered:The importance of proof and the power of modelingThe arts of the Quadrivium and their perspectives on cosmic orderThe role of rhetoric and logic in the study of mathematicsEngaging the senses in the experience of learning mathematicsThe transformation of students' perceptions of mathematics through an encounter with the QuadriviumToday's Guest:Peter Ulrickson is a professor of mathematics at the Catholic University of America. In addition to his work on the quadrivium, he publishes original research in various areas of modern mathematics. Professor Ulrickson received his Ph.D. from the University of Notre Dame.For more information about the books: briefquadrivium.comTimestamps:00:00 Introduction03:28 Introduction to A Brief Quadrivium04:07 Exploring Music and Astronomy in the Quadrivium10:01 Proof and Modeling in Mathematics13:09 Developing the Sense for Order20:45 Engaging the Senses in Mathematical Inquiry26:51 The Ordering of the Quadrivial Arts30:48 Exploring the Teacher's GuideResources Mentioned in Today's Episode:Peter Ulrickson, A Brief Quadrivium (publisher, Amazon) and Teaching the Quadrivium (publisher, Amazon)"The Quadrivium and the Stakes for Ordering the Mathematical Arts" by Lesley-Anne Dyer WilliamsUniversity of Dallas Links:Classical Education Master's Program at the University of Dallas: udallas.edu/classical-edSt. Ambrose Center Professional Development for Teachers and Administrators: https://k12classical.udallas.edu/Support the showIf you enjoyed the show, please leave a rating and review — it helps others find us!

In 1961, a young couple boarded a ship to Vienna with nothing but faith, a suitcase, and an “impossible dream”—to bring the Word of God into the most spiritually restricted places on earth. What began with handwritten Scripture, smuggled Bibles, and hidden church meetings has become a sweeping movement of Gospel transformation across Eastern Europe and beyond.The Impossible Dream takes you deep into the heart of that mission, sharing firsthand accounts of courage, smuggling, sacrifice, and the miraculous power of Scripture. Through riveting stories witness how God's Word made its way past secret police, prison walls, and warzones—straight into the hearts of those who needed it most Dirk Smith Vice President Dirk Smith joined Eastern European Mission following his highly successful tenure as a development officer with his alma mater, Harding University. An accomplished manager, he earned experience in business development with an eye for revenue building through positions with firms like Jackson & Coker in Dallas, Texas, and T. Williams Consulting serving clients in Pennsylvania, New Jersey and New York. He has a bachelor's degree in Mathematics and an MBA with a focus on Organizational Development and Ethics. At EEM, Dirk oversees fundraising and marketing efforts as well as assists with U.S. operations. He is an experienced presenter and storyteller and loves sharing the stories of what God is doing through the ministry of EEM.WebsiteInstagramAmazon

Watch the Q&A session here: https://youtu.be/Lv5h-Pp1r6sLooking at the plant world, one discovers beautiful and fascinating structures in the shape and arrangement of leaves, stems and roots. Some are simple and symmetric, other features are arranged in elegant Fibonacci spirals, yet others exhibit fractal-like patterns. How are these structures created with such regularity and reproducibility? Such arrangements often follow simple rules that we can fully understand mathematically.This lecture was recorded by Alain Goriely on 11th November 2025 at Barnard's Inn Hall, London.Professor Alain Goriely FRS is Gresham Professor of Geometry.He is also a mathematician known for dynamical systems, mathematical biology, and mechanics. He developed the mathematical theory of biological growth and is Director of the Oxford Centre for Industrial and Applied Mathematics. His work spans plant tendrils, seashells, umbilical cords, brain modelling, and applied mathematics outreach.The transcript and downloadable versions of the lecture are available from the Gresham College website: https://www.gresham.ac.uk/watch-now/shape-plantsGresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: https://gresham.ac.uk/support/Website:  https://gresham.ac.ukTwitter:  https://twitter.com/greshamcollegeFacebook: https://facebook.com/greshamcollegeInstagram: https://instagram.com/greshamcollegeSupport the show

December 12, 2025 - Zach and Asheef discuss the current landscape of international value investing, focusing on the unique perspectives that come from investing outside the US.Asheef Lalani as an independent director to the board of Sailfish Royalty Corp. Mr. Lalani graduated from the University of Waterloo with a Bachelor of Mathematics and Masters of Accounting, earned the CA/CPA designation in 2002 and is a CFA charterholder since 2003. Asheef first started his career with PricewaterhouseCoopers in 1998 and went on to become a portfolio manager at UBS Securities. Currently, Mr. Lalani is the Chief Investment Officer at Berczy Park Capital – a private family office in Toronto, Canada.

Amy Boros and Shari Insley teach middle school science in different parts of the state, but they share a passion for bringing the real world into their classrooms for their students. Over the summer, the Perrysburg Education Association member and the North Olmsted Education Association member shared grant funding to travel far out into the real world for a once-in-a-lifetime learning experience that will enhance their students' learning for years to come. On this episode, they share how they're using what they saw and did in Iceland to help their students learn and grow in Ohio, and their advice for other educators who want to experience this kind of real-world professional development for themselves.SEE THE HIGHLIGHTS | Click here to see some of Shari's photos from the Fund for Teachers fellowship in Iceland. Click here to see Amy's highlights from the trip. EXPLORE THE OPPORTUNITIES | Amy and Shari mentioned several grants and learning opportunities available to Ohio science educators. See the following links for more information about some of them:Fund For Teachers Grant  Teacher Air Camp  Yellowstone Educator Opportunity Summer 2026 Amy and Shari also shared an OEA Technology Grant to buy cameras and go pros to use on their trip and in their classrooms back home. Please note, OEA is in the process of redeveloping and streamlining the Affiliate Grant Program, and as part of the transition, no applications are being accepted for Technology Grants for the 2025-26 cycle. Make sure you listen to Episode 16 of Public Education Matters to learn more on the OEA grants being offered right now.SHARE YOUR THOUGHTS | If you'd like to share your feedback on the Public Education Matters podcast, including your ideas for what you'd like to hear about - or talk about - on future episodes, please email educationmatters@ohea.org. SUBSCRIBE | Click here to subscribe to Public Education Matters on Apple Podcasts or click here to listen on Spotify so you don't miss a thing. You can also find Public Education Matters on many other platforms. Click here for some of those links so you can listen anywhere. And don't forget you can listen to all of the previous episodes anytime on your favorite podcast platform, or by clicking here.Featured Public Education Matters guests: Amy Boros, Perrysburg Education Association memberAmy Boros teaches 5th and 6th grade Science at Hull Prairie Intermediate School in Perrysburg. She has experience in classroom teaching at the elementary, middle school and collegiate levels; educational classroom technology; grant researching, authoringand evaluation, as well as educational consulting and conference presentations in both mathematics and science. With degrees from Bowling Green State University and the University of Toledo, Amy is currently in her 30th year in education.Amy is an accomplished grant writer who has been awarded thousands of dollars in grants for her classroom, school, district, and outside organizations. In addition, Amy has authored several articles about middle school science education in Science Scope Journal and Science and Children Journal, publications of The National Science Teachers Association.In 2019, Amy was invited to participate in an extensive research project onboard the Lake Guardian, an EPA research vessel on Lake Erie; selected as one of 15 educators to collect data alongside scientists. While on board, she evaluated the presence ofmicroplastics, toxic algae and microbial organisms in surface water and sediment throughout Lake Erie's basins.She continues to work alongside scientists by helping with research, most recently in Costa Rica and Yellowstone National Park.Amy was awarded the 2022 President's Innovation Award in Environmental Education, a joint award from the White House and the EPA for her environmental education work inside and outside of the classroom.Shari Insley, North Olmsted Education Association memberShari Insley is a middle school math and science teacher for North Olmsted City Schools with 20 years of experience in education. Of her 20 years in education, the past 18 years have been dedicated to North Olmsted, and her first 2 years were spent teaching in Gallup, New Mexico.Shari earned a B.S. in Middle Childhood Education in Mathematics and Science and a Master's degree in Curriculum and Teaching from Bowling Green State University in Bowling Green, Ohio. In addition to her teaching expertise, Shari was honored as the recipient of the 2024 Presidential Innovation Award for Environmental Educators. She has also served on the Strategic Planning Committee for the Science Education Council of Ohio the past 2 years.Since 2016, Shari has dedicated her summers to participating in educator courses to expand her knowledge of freshwater ecosystems in the Great Lakes. She has taken part in grant opportunities through Ohio Sea Grant at The Ohio State University's Stone Laboratory, sailed aboard the R/V Lake Guardian with the EPA, and worked with the Gelfand STEM Center at Case Western Reserve University. Most recently, Shari was awarded a Fund for Teachers grant to travel to Iceland in the summer of 2025, where she explored the country's unique geothermal and glacial environments to enrich her environmental science curriculum.Connect with OEA:Email educationmatters@ohea.org with your feedback or ideas for future Public Education Matters topicsLike OEA on FacebookFollow OEA on TwitterFollow OEA on InstagramGet the latest news and statements from OEA hereLearn more about where OEA stands on the issues Keep up to date on the legislation affecting Ohio public schools and educators with OEA's Legislative WatchAbout us:The Ohio Education Association represents nearly 120,000 teachers, faculty members and support professionals who work in Ohio's schools, colleges, and universities to help improve public education and the lives of Ohio's children. OEA members provide professional services to benefit students, schools, and the public in virtually every position needed to run Ohio's schools.Public Education Matters host Katie Olmsted serves as Media Relations Consultant for the Ohio Education Association. S...

It's YOUR time to #EdUpIn this episode, part of our Academic Integrity Series, sponsored by ⁠Integrity4EducationYOUR guest is W. Ila Peterson, Professor of Mathematics & Director of Faculty Development, Arizona Western CollegeYOUR cohost is Thomas Fetsch, CEO, Integrity4EducationYOUR host is ⁠Elvin Freytes⁠How is Arizona Western College serving approximately 8,000 students across Yuma & La Paz County with online education while maintaining academic integrity, & why does Ila believe AI breaks down language barriers for their Hispanic serving institution?What creative faculty responses is Ila seeing like podcast style presentations instead of essays, 30 to 45 minute "technology snack" PD sessions on tools like Notebook LM, & why does she believe faculty ingenuity is key to adapting to AI?How does Arizona Western's current policy leave AI decisions to individual faculty with required syllabus statements, what institutional AI governance principles are being drafted for the next year, & why does Ila believe this is the 1st moment we're truly training students for jobs that don't yet exist?Listen in to #EdUpThank YOU so much for tuning in. Join us on the next episode for YOUR time to EdUp!Connect with YOUR EdUp Team - ⁠⁠⁠⁠⁠ ⁠⁠⁠⁠⁠Elvin Freytes⁠⁠⁠⁠⁠⁠⁠⁠⁠ ⁠& ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ Dr. Joe Sallustio⁠⁠⁠⁠⁠● Join YOUR EdUp community at ⁠The EdUp Experience⁠We make education YOUR business!P.S. Want to get early, ad-free access & exclusive leadership content to help support the show? Then ⁠⁠​subscribe today​⁠⁠ to lock in YOUR $5.99/m lifetime supporters rate! This offer ends December 31, 2025!

Learning to teach mathematics better with Ariel Beggs, program coordinator, professional development facilitator, and Presidential Award winning educator. Ariel shares her journey from two decades of middle school mathematics teaching to supporting mathematics educators through the University of Arizona Center for Recruitment and Retention of Mathematics Teachers. Throughout the conversation, she highlights the power of supportive relationships, noting the difference between toxic and tolerable stress is the presence of community and connection, and how this belief shapes her coaching, collaboration, and leadership. Links from the episode Center of Recruitment and Retention of Mathematics Teachers (CRR) (https://crr.math.arizona.edu/) ReEngaging Aspirational Learners (Getting REAL) (https://crr.math.arizona.edu/getting-real) Mathematics Educator Appreciation Day Conference (MEAD) (https://crr.math.arizona.edu/mead-conference) TODOS: Mathematics for ALL (https://www.todos-math.org/) Teaching Math Teaching Episode 99 - Rodrigo Gutiérrez and Melissa Hosten: Being Responsive and Engaged to Elevate the Work of Math Teachers (https://www.teachingmathteachingpodcast.com/99) Teaching Math Teaching Episode 116 - Marian Dingle: You Teach Who You Are (https://www.teachingmathteachingpodcast.com/116) Coaching the 5 Practices (https://www.corwin.com/books/coaching-the-5-practices-287127?srsltid=AfmBOooUWNugdxYQl2YERZudkbpjkxohjun78q96FBdqRAeYL6q9S073) Powerful Mathematicians Who Changed the World from A to Z (https://www.nctm.org/Store/Products/Powerful-Mathematicians-Who-Changed-the-World-from-A-to-Z/) Reimagining the Mathematics Classroom (https://www.nctm.org/Store/Products/Reimagining-the-Mathematics-Classroom/) The Anxious Generation (https://bookshop.org/a/1964/9780593655030) What Video Games Have to Teach Us About Learning and Literacy. (https://bookshop.org/a/1964/9781403984531) Special Guest: Ariel Beggs.

Ready to learn the history, philosophy, and practice of an experienced professional in the test prep industry? MEET OUR GUEST Meet Angie Kelley. Angie is the founder of Land Run Learning, a test prep and tutoring company dedicated to helping high-performing students train smart, test strong, and claim their futures. A licensed Oklahoma educator and graduate of Oklahoma Christian University with a B.S.E. in Mathematics, Angie draws on twenty years of classroom experience and a passion for strategic learning to help students reach their potential on high-stakes exams. Her work bridges the gap between academic mastery and confident performance, empowering students to thrive under pressure. Find Angie at angie@landrunlearning.com. ABOUT THIS PODCAST Tests and the Rest is THE college admissions industry podcast. Explore all of our episodes on the show page. ABOUT YOUR HOSTS Mike Bergin is the president of Chariot Learning and founder of TestBright, Roots2Words, and College Eagle. Amy Seeley is the president of Seeley Test Pros and LEAP. If you're interested in working with Mike and/or Amy for test preparation, training, or consulting, get in touch through our contact page.  

Chris Holman welcomes back Sean Cervantes – Business Development & Growth Officer at LAFCU, Lansing, MI. Welcome Sean, remind everyone about LAFCU? Sean, you've been in your role since the Spring, how are things going? Recent news for LAFCU: being Nationally Recognized as a 2025 Best Place to Work for Women, tell us about that? LAFCU's CFO Leslie Rorie was Honored with a 2025 Real McCoy Award in Mathematics talk about that? Big community event last month for LAFCU, Heritage Day 2025 how did that go? » Visit MBN website: www.michiganbusinessnetwork.com/ » Subscribe to MBN's YouTube: www.youtube.com/@MichiganbusinessnetworkMBN » Like MBN: www.facebook.com/mibiznetwork » Follow MBN: twitter.com/MIBizNetwork/ » MBN Instagram: www.instagram.com/mibiznetwork/

In this episode, Dean takes the host's chair to interview Maegan and Kyle, who have both recently co-authored books in the Building Thinking Classrooms series with Peter Liljedahl. They discuss the release of the new Building Thinking Classrooms Tasks in Mathematics, Grades 6-12 book and how it complements Maegan's previously released Building Thinking Classrooms Tasks in Mathematics, Grades K-5. Together, the group explores the process of selecting tasks, the importance of thin-slicing, and why the pedagogical research found in the rest of the book is just as critical as the tasks themselves. They also open up about the vulnerability required to write these resources, including the realization that even experienced teachers often need to relearn math concepts to teach them effectively. Tune in for a behind-the-scenes look at creating these resources and how they can support your journey in the classroom.Links:⁠Building Thinking Classrooms Tasks in Mathematics, Grades K-5⁠Building Thinking Classrooms Tasks in Mathematics, Grades 6-12Saskatchewan Understand Math Conference 2026

In this fascinating episode, Amb. Elisha sits down with renowned composer, pianist, educator, and music theorist Kurt Ellenberger

Episode: 1484 Georg Cantor, the man who counted beyond infinity.  Today, we wonder about counting to infinity.

Jacob Barandes is Senior Preceptor in Physics at Harvard University, where he works widely across the philosophy of physics, with focuses on the foundations of quantum mechanics, the philosophy of spacetime, and the metaphysics of laws. In this episode, Robinson and Jacob focus on the foundations of quantum mechanics. They discuss the importance of history and philosophy in the same, its connections to mathematics, many of the biggest puzzles in quantum physics, and Jacob's new approach to the foundations, which he refers to as the “Indivisibility” approach.Jacob's Website: https://www.jacobbarandes.comOUTLINE00:00 Mathematics, Nature, and Physics07:55 The Deep Link Between Math and Physics CLIP15:21 Scrutinizing the History and Philosophy of Physics28:11 A Digression on Achille Varzi36:53 The Etymology of “Matrix”41:17 Learning from the History of Physics52:38 Why Does Quantum Mechanics Need New Foundations?59:04 Does Quantum Gravity Need New Quantum Foundations?01;08:26 What Is a Constructive Physical Theory?01:32:31 Markov Laws and Determinism01:45:30 The Wave Function02:06:53 Inconsistencies in Quantum Mechanics02:12:20 What Is Quantum Decoherence?02:23:10 The Biggest Problems in Quantum Foundations?02:33:49 Interpretations of Quantum Mechanics02:38:57 Quantum Mechanics, Many Worlds, and the Problem of Induction02:50:05 The Indivisibility Interpretation of Quantum Mechanics03:04:42 What Are the Fundamentalia of the Universe?Robinson's Website: http://robinsonerhardt.comRobinson Erhardt researches symbolic logic and the foundations of mathematics at Stanford University, where he is also a JD candidate in the Law School.

Tutita Casa, Anna Strauss, Jenna Waggoner & Mhret Wondmagegne, Developing Student Agency: The Strategy Showcase ROUNDING UP: SEASON 4 | EPISODE 7 When students aren't sure how to approach a problem, many of them default to asking the teacher for help. This tendency is one of the central challenges of teaching: walking the fine line between offering support and inadvertently cultivating dependence.  In this episode, we're talking with a team of educators about a practice called the strategy showcase, designed to foster collaboration and help students engage with their peers' ideas.  BIOGRAPHIES Tutita Casa is an associate professor of elementary mathematics education at the Neag School of Education at the University of Connecticut. Mhret Wondmagegne, Anna Strauss, and Jenna Waggoner are all recent graduates of the University of Connecticut School of Education and early career elementary educators who recently completed their first years of teaching. RESOURCE National Council of Teachers of Mathematics  TRANSCRIPT Mike Wallus: Well, we have a full show today and I want to welcome all of our guests. So Anna, Mhret, Jenna, Tutita, welcome to the podcast. I'm really excited to be talking with you all about the strategy showcase. Jenna Waggoner: Thank you.  Tutita Casa: It's our pleasure.  Anna Strauss: Thanks.  Mhret Wondmagegne: Thank you. Mike: So for listeners who've not read your article, Anna, could you briefly describe a strategy showcase? So what is it and what could it look like in an elementary classroom? Anna: So the main idea of the strategy showcase is to have students' work displayed either on a bulletin board—I know Mhret and Jenna, some of them use posters or whiteboards. It's a place where students can display work that they've either started or that they've completed, and to become a resource for other students to use. It has different strategies that either students identified or you identified that serves as a place for students to go and reference if they need help on a problem or they're stuck, and it's just a good way to have student work up in the classroom and give students confidence to have their work be used as a resource for others. Mike: That was really helpful. I have a picture in my mind of what you're talking about, and I think for a lot of educators that's a really important starting point.  Something that really stood out for me in what you said just now, but even in our preparation for the interview, is the idea that this strategy showcase grew out of a common problem of practice that you all and many teachers face. And I'm wondering if we can explore that a little bit. So Tutita, I'm wondering if you could talk about what Anna and Jenna and Mhret were seeing and maybe set the stage for the problem of practice that they were working on and the things that may have led into the design of the strategy showcase. Tutita: Yeah. I had the pleasure of teaching my coauthors when they were master's students, and a lot of what we talk about in our teacher prep program is how can we get our students to express their own reasoning? And that's been a problem of practice for decades now. The National Council of Teachers of Mathematics has led that work. And to me, [what] I see is that idea of letting go and really being curious about where students are coming from. So that reasoning is really theirs. So the question is what can teachers do? And I think at the core of that is really trying to find out what might be limiting students in that work. And so Anna, Jenna, and Mhret, one of the issues that they kept bringing back to our university classroom is just being bothered by the fact that their students across the elementary grades were just lacking the confidence, and they knew that their students were more than capable. Mike: Jenna, I wonder if you could talk a little bit about, what did that actually look like? I'm trying to imagine what that lack of confidence translated into. What you were seeing potentially or what you and Anna and Mhret were seeing in classrooms that led you to this work. Jenna: Yeah, I know definitely we were reflecting, we were all in upper elementary, but we were also across grade levels anywhere from fourth to fifth grade all the way to sixth and seventh. And across all of those places, when we would give students especially a word problem or something that didn't feel like it had one definite answer or one way to solve it or something that could be more open-ended, we a lot of times saw students either looking to teachers. "I'm not sure what to do. Can you help me?" Or just sitting there looking at the problem and not even approaching it or putting something on their paper, or trying to think, "What do I know?" A lot of times if they didn't feel like there was one concrete approach to start the problem, they would shut down and feel like they weren't doing what they were supposed to or they didn't know what the right way to solve it was. And then that felt like kind of a halting thing to them. So we would see a lot of hesitancy and not that courage to just kind of be productively struggling. They wanted to either feel like there was something to do or they would kind of wait for teacher guidance on what to do. Mike: So we're doing this interview and I can see Jenna and the audience who's listening, obviously Jenna, they can't see you, but when you said "the right way," you used a set of air quotes around that. And I'm wondering if you or Anna or Mhret would like to talk about this notion of the right way and how when students imagined there was a right way, that had an effect on what you saw in the classroom. Jenna: I think it can be definitely, even if you're working on a concept like multiplication or division, whatever they've been currently learning, depending on how they're presented instruction, if they're shown one way how to do something but they don't understand it, they feel like that's how they're supposed to understand to solve the problem. But if it doesn't make sense for them or they can't see how it connects to the problem and the overall concept, if they don't understand the concept for multiplication, but they've been taught one strategy that they don't understand, they feel like they don't know how to approach it. So I think a lot of it comes down to they're not being taught how to understand the concept, but they're more just being given one direct way to do something. And if that doesn't make sense to them or they don't understand the concepts through that, then they have a really difficult time of being able to approach something independently. Mike: Mhret, I think Jenna offered a really nice segue here because you all were dealing with this question of confidence and with kids who, when they didn't see a clear path or they didn't see something that they could replicate, just got stuck, or for lack of a better word, they kind of turned to the teacher or imagined that that was the next step. And I was really excited about the fact that you all had designed some really specific features into the strategy showcase that addressed that problem of practice. So I'm wondering if you could just talk about the particular features or the practices that you all thought were important in setting up the strategy showcase and trying to take up this practice of a strategy showcase. Mhret: Yeah, so we had three components in this strategy showcase. The first one, we saw it being really important, being open-ended tasks, and that combats what Jenna was saying of "the right way." The questions that we asked didn't ask them to use a specific strategy. It was open-ended in a way that it asked them if they agreed or disagreed with a way that someone found an answer, and it just was open to see whatever came to their mind and how they wanted to start the task. So that was very important as being the first component.  And the second one was the student work displayed, which Anna was talking about earlier. The root of this being we want students' confidence to grow and have their voices heard. And so their work being displayed was very important—not teacher work or not an example being given to them, but what they had in their mind. And so we did that intentionally with having their names covered up in the beginning because we didn't want the focus to be on who did it, but just seeing their work displayed—being worth it to be displayed and to learn from—and so their names were covered up in the beginning and it was on one side of the board.  And then the third component was the students' co-identified strategies. So that's when after they have displayed their individual work, we would come up as a group and talk about what similarities did we see, what differences in what the students have used. And they start naming strategies out of that. They start giving names to the strategies that they see their peers using, and we co-identify and create this strategy that they are owning. So those are the three important components. Mike: OK. Wow. There's a lot there. And I want to spend a little bit of time digging into each one of these and I'm going to invite all four of you to feel free to jump in and just let us know who's talking so that everybody has a sense of that.  I wonder if you could talk about this whole idea that, when you say open-ended tasks, I think that's really important because it's important that we build a common definition. So when you all describe open-ended tasks, let's make sure that we're talking the same language. What does that mean? And Tutita, I wonder if you want to just jump in on that one. Tutita: Sure. Yeah. An open-ended task, as it suggests, it's not a direct line where, for example, you can prompt students to say, "You must use 'blank' strategy to solve this particular problem." To me, it's just mathematical. That's what a really good rich problem is, is that it really allows for that problem solving, that reasoning. You want to be able to showcase and really gauge where your students are. Which, as a side benefit, is really beneficial to teachers because you can formatively assess where they're even starting with a problem and what approaches they try, which might not work out at first—which is OK, that's part of the reasoning process—and they might try something else. So what's in their toolbox and what tool do they reach for first and how do they use it? Mike: I want to name another one that really jumped out for me. I really—this was a big deal that everybody's strategy goes up. And Anna, I wonder if you can talk about the value and the importance of everybody's strategy going up. Why did that matter so much? Anna: I think it really helps, the main thing, for confidence. I had a lot of students who in the beginning of starting the strategy showcase would start kind of like at least with a couple ideas, maybe a drawing, maybe they outlined all of the numbers, and it helps to see all of the strategies because even if you are a student who started out with maybe one simple idea and didn't get too far in the problem, seeing up on the board maybe, "Oh, I have the same beginning as someone else who got farther into the problem." And really using that to be like, "I can start a problem and I can start with different ideas, and it's something that can potentially lead to a solution." So there is a lot of value in having all of the work that everyone did because even something that is just the beginning of a solution, someone can jump in and be like, "Oh, I love the way that you outlined that," or "You picked those numbers first to work on. Let's see what we can use from the way that you started the problem to begin to work on a solution." So in that way, everyone's voice and everyone's decisions have value. And even if you just start off with something small, it can lead to something that can grow into a bigger solution. Mike: Mhret, can I ask you about another feature that you mentioned? You talked about the importance, at least initially, of having names removed from the work. And I wonder if you could just expand on why that was important and maybe just the practical ways that you managed withholding the names, at least for some of the time when the strategy showcase was being set up. Can you talk about both of those please? Mhret: Yes, yeah. I think all three of us when we were implementing this, we—all kids are different. Some of them are very eager to share their work and have their name on it. But we had those kids that maybe they just started with a picture or whatever it may be. And so we saw their nerves with that, and we didn't want that to just mask that whole experience. And so it was very important for us that everybody felt safe. And later we'll talk about group norms and how we made it a safe space for everyone to try different strategies. But I think not having their names attached to it helped them focus not on who did it, but just the process of reasoning and doing the work. And so we did that practically I think in different ways, but I just use tape, masking tape to cover up their names. I know some of—I think maybe Jenna, you wrote their names on the back of the paper instead of the front. But I think a way to not make the name the focus is very important. And then hopefully by the end of it, our hope is that they would gain more confidence and want to name their strategy and say that that is who did it. Mike: I want to ask a follow up about this because it feels like one of the things that this very simple, but I think really important, idea of withholding who created the strategy or who did the work. I mean, I think I can say during my time in classrooms when I was teaching, there are kids that classmates kind of saw as really competent or strong in math. And I also know that there were kids who didn't think they were good at math or perhaps their classmates didn't think were good at math. And it feels like by withholding the names that would have a real impact on the extent to which work would be considered as valuable. Because you don't know who created it, you're really looking at the work as opposed to looking at who did the work and then deciding whether it's worth taking up. Did you see any effects like that as you were doing this? Jenna: This is Jenna. I was going to say, I know for me, even once the names were removed, you would still see kids sometimes want to be like, "Oh, who did this?" You could tell they still are almost very fixated on that idea of who is doing the work. So I think by removing it, it still was definitely good too. With time, they started to less focus on "Who did this?" And like you said, it's more taking ownership if they feel comfortable later down the road. But sometimes you would have, several students would choose one approach, kind of what they've seen in classrooms, and then you might have a few other slightly different, of maybe drawing a picture or using division and connecting it to multiplication. And then you never wanted those kids to feel like what they were doing was wrong. Even if they chose the wrong operation, there was still value in seeing how that was connected to the problem or why they got confused. So we never wanted one or two students also to feel individually focused on if maybe what they did initially—not [that it] wasn't correct, but maybe was leading them in the wrong direction, but still had value to understand why they chose to do that. So I think just helping, again, all the strategies work that they did feel valuable and not having any one particular person feel like they were being focused on when we were reflecting on what we put up on display. Mike: I want to go back to one other thing that, Mhret, you mentioned, and I'm going to invite any of you, again, to jump in and talk about this, but this whole idea that part of the prompting that you did when you invited kids to examine the strategies was this question of do you agree or do you disagree? And I think that's a really interesting way to kind of initiate students' reflections. I wonder if you can talk about why this idea of, "Do you agree or do you disagree" was something that you chose to engage with when you were prompting kids? And again, any of you all are welcome to jump in and address this, Anna: It's Anna. I think one of the reasons that we chose to [have them] agree or disagree is because students are starting to look for different ways to address the problem at hand. Instead of being like, "I need to find this final number" or "I need to find this final solution," it's kind of looking [at], "How did this person go about solving the problem? What did they use?" And it gives them more of an opportunity to really think about what they would do and how what they're looking at helps in any way. Jenna: And then this is Jenna. I was also going to add on that I think by being "agree or disagree" versus being like, "yes, I got the same answer," and I feel like the conversation just kind of ends at that point. But they could even be like, "I agree with the solution that was reached, but I would've solved it this way, or my approach was different." So I think by having "agree or disagree," it wasn't just focusing on, "yes, this is the correct number, this is the correct solution," and more focused on, again, that approach and the different strategies that could be used to reach one specific solution that was the answer or the correct thing that you're looking for. Tutita: And this is Tutita, and I agree with all of that. And I can't help but going back just to the word "strategy," which really reflects students' reasoning, their problem solving, argumentation. It's really not a noun; it's a verb. It's a very active process. And sometimes we, as teachers, we're so excited to have our students get the right answer that we forget the fun in mathematics is trying to figure it out.  And I can't help but think of an analogy. So many people love to watch sports. I know Jenna's a huge UConn women's basketball… Jenna: Woohoo! Tutita: …fan, big time. Or if you're into football, whatever it might be, that there's always that goal. You're trying to get as many more points, and as many as you can, more points than the other team. And there are a lot of different strategies to get there, but we appreciate the fact that the team is trying to move forward and individuals are trying to move forward. So it's that idea with the strategy, we need to as teachers really open up that space to allow that to come out and progressively—in the end, we're moving forward even though within a particular time frame, it might not look like we are quite yet. I like the word "yet." But it's really giving students the time that they need to figure it out themselves to deepen their understanding. Mike: Well, I will say as a former Twin Cities resident, I've watched Paige Bueckers for a long time, and… Tutita: There we go. Mike: …in addition to being a great shooter, she's a pretty darn good passer and moves the ball.  And in some ways that kind of connects with what you all are doing with kids, which is that—moving ideas around a space is really not that different from moving the ball in basketball. And that you have the same goal in scoring a basket or reaching understanding, but it's the exchange that are actually the things that sometimes makes that happen. Jenna: I love it. Thank you.  Tutita: Nice job. Mike: Mhret, I wanted to go back to this notion that you were talking about, which is co-naming the strategies as you were going through and reflecting on them. I wonder if you could talk a little bit about, what does co-naming mean and why was it important as a part of the process? Mhret: Mm-hmm. Yeah. So, I think the idea of co-naming and co-identifying the strategies was important. Just to add on to the idea, we wanted it all to be about the students and their voice, and it's their strategy and they're discussing and coming up with everything. And we know of the standard names of strategies like standard algorithm or whatever, but I think it gave them an extra confidence when it was like, "Oh, we want to call it—" I forgot the different names that they would come up with for strategies. Jenna: I think they had said maybe "stacking numbers," something like that. They would put their own words. It wasn't standard algorithm, but like, "We're going to stack the numbers on top of each other," I think was maybe one they had said. Mhret: Mm-hmm. So I think it added to that collaboration within the group that they were in and also just them owning their strategy. And so, yeah. Mike: That leads really nicely into my next question. And Anna, this is one I was going to pose to you, but everyone else is certainly welcome to contribute.  I'm wondering if you could talk a little bit about what happened when you all started to implement this strategy showcase in your classroom. So what impacts did you see on students' efficacy, their confidence, the ways that they collaborated? Could you talk a little bit about that? Anna: So I think one of the biggest things that I saw that I was very proud of was there was less of a need for me to become part of the conversation as the teacher because students were more confident to build off of each other's ideas instead of me having to jump in and be like, "Alright, what do we think about what this person did?" Students, because their work became more anonymous and because everyone was kind of working together and had different strategies, they were more open to discussing with each other or working off of each other's ideas because it wasn't just, "I don't know how to do this strategy." It was working together to really put the pieces together and come to a final agree or disagree.  So it really helped me almost figure out where students are, and it brought the confidence into the students without me having to step in and really officiate the conversation. So that was the really big thing that I saw at least in some of my groups, was that huge confidence and more communication happening. Mhret: Yeah. This is Mhret. I think it was very exciting too, like Anna was saying, that—them getting excited about their work, and everything up on the board is their work. And so seeing them with a sticky note, trying to find the similarities and differences between strategies, and getting excited about what someone is doing, I think that was a very good experience and feeling for me because of the confidence that I saw grow through the process of the kids, but also the collaboration of, "It's OK to use what other people know to build upon the things that I need to build upon." And so I think it just increased collaboration, which I think is really important when we talk about reasoning and strategies. Mike: Which actually brings me to my next question, and Jenna, I was wondering if you could talk a little bit about: What did you see in the ways that students were reasoning around the mathematics or engaging in problem solving? Jenna: Yeah, I know one specific example that stood out was—again, that initial thing of when we gave a student a problem, they would look to the teacher and a little bit later on in the process when giving a problem, we had done putting the strategies up, we'd cocreated the names, and then they were trying a similar problem independently. And one of my students right off the bat had that initial reaction that we would've seen a few weeks ago of being like, "I don't know what to do." And she put a question mark on the paper. So I gave her a minute and then she looked at me and I said, "Look at this strategy. Look at what you and your classmates have done to come together." And then she got a little redirection, but it wasn't me telling her what to do. And from there I stepped away and let her just reference that tool that was being displayed. And from there, she was able to show her work, she was able to choose a strategy she wanted to do, and she was able to give her answer of whether she agreed or disagreed on what she had seen. So I think it was just again, that moment of realizing that what I needed to step in and do was a lot smaller than it had previously been, and she could use this tool that we had created together and that she had created with her peers to help her answer that question. Anna: I think to add onto that, it's Anna, there was a huge spike in efficiency as well because all these different strategies were being discovered and brought to light and put onto the strategy showcase. Maybe if we're talking about multiplication, if some student had repeated addition in the beginning and they're repeatedly adding numbers together to find a multiplication product, they're realizing, "Oh my goodness, I can do this so much more efficiently if I use this person's strategy or if I try this one instead." And it gives them the confidence to try different things. Instead of getting stuck in the rut of saying, "This is my strategy and this is the way that I'm going to do it," they became a little more explorative, and they wanted to try different things out or maybe draw a picture and use that resource to differentiate their math experience. Mike: I want to mark something here that seems meaningful, which is this whole notion that you saw this spike. But the part that I'm really contemplating is when you said kids were less attached to, "This is my strategy" and more willing to adopt some of the ideas that they saw coming out of the group. That feels really, really significant, both in terms of how we want kids to engage in problem solving and also in terms of efficacy. That really I think is one to ponder for folks who are listening to the podcast, is the effect on students' ability to be more flexible in adopting ideas that may not have been theirs to begin with. Thank you for sharing that. Anna.  I wonder if you could also spend a bit of time talking about some of the ways that you held onto or preserve the insights and the strategies that emerged during a showcase. Are there artifacts or ways that a teacher might save what came from a strategy showcase for future reference? Anna: So, I think the biggest thing as a takeaway and something to hold onto as a teacher who uses the strategy showcase is the ability to take a step back and allow students to utilize the resources that they created. And I think something that I used is I had a lot of intervention time and time where students were able to work in small groups and work together in teams and that sort of thing, keeping their strategies and utilizing them in groups. Remember when this person brought up this strategy, maybe we can build off of that and really utilizing their work and carrying it through instead of just putting it up and taking it down and putting up another one. Really bringing it through. And any student work is valuable. Anything that a student can bring to the table that can be used in the future, like holding onto that and re-giving them that confidence. "Remember when this person brought up that we can use a picture to help solve this problem?" Bringing that back in and recycling those ideas and bringing back in not just something that the teacher came up with, but what another student came up with, really helps any student's confidence in the classroom. Mike: So I want to ask a question, and Tutita and Mhret, I'm hoping you all can weigh in on this. If an educator wanted to implement the strategy showcase in their classroom, I want to explore a bit about how we could help them get started. And Tutita, I think I want to start with you and just say from a foundational perspective of building the understanding that helps support something like a strategy showcase, what do you think is important? Tutita: I actually think there are two critical things. The first is considering the social aspect and just building off of what Anna was saying is, if you've listened carefully, she's really honoring the individual. So instead of saying, "Look," that there was this paper up there—as teachers, we have a lot on our walls—it's actually naming the student and honoring that student, even though it's something that as a teacher, you're like, "Yes, someone said it! I want them to actually think more about that." But it's so much more powerful by giving students the credit for the thinking that they're doing to continue to advance that. And all that starts with assuming that students can. And oftentimes at the elementary level, we tend to overlook that. They're so cute—especially those kindergartens, pre-K, kindergarten—but it's amazing what they can do. So if you start with assuming that they can and waiting for their response, then following up and nurturing that, I think you as teachers will get so much more from our students and starting with that confidence. And that brings me to the next point that I think listeners who teach in the upper elementary grades or maybe middle school or high school might be like, "Oh, this sounds great. I'll start with them." But I want to caution that those students might be even more reticent because they might think that to be a good math student, you're supposed to know the answer, you're supposed to know it quickly, and there's one strategy you're supposed to use. And so, in fact, I would argue that probably those really cute pre-K and kindergartners will probably be more open because if anyone has asked a primary student to explain what they have down on paper, 83 minutes later, the story will be done.  And so it might take time. You have to start with that belief and just really going with where your class and individuals are socially. Some of them might not care that you use their name. Others might, and that might take time. So taking the time and finding different ways to stay with that belief and make sure that you're transferring it to students once they have it. As you can hear, a lot of what my coauthors mentioned, then they take it from there. But you have to start with that belief at the beginning that elementary students can. Mike: Mhret, I wonder if you'd be willing to pick up on that, because I find myself thinking that the belief aspect of this is absolutely critical, and then there's the work that a teacher does to build a set of norms or routines that actually bring that belief to life, not only for yourself but for students. I wonder if you could talk about some of the ways that a teacher might set up norms, set up routines, maybe even just set up their classroom in ways that support the showcase. Mhret: Yeah. So practically, I think for the strategy showcase, an important aspect is finding a space that's accessible to students because we wanted them to be going back to it to use it as a resource. So some of us used a poster board, a whiteboard, but a vertical space in the room where students can go and see their work up I think is really important so that the classroom can feel like theirs. And then we also did a group norm during our first meeting with the kids where we co-constructed group norms with the kids of like, "What does it look like to disagree with one another?" "If you see a strategy that you haven't used, how can you be kind with our words and how we talk about different strategies that we see up there?" I think that's really important for all grades in elementary because some kids can be quick to their opinions or comments, and then providing resources that students can use to share their idea or have their idea on paper I think is important. If that's sticky notes, a blank piece of paper, pencils, just practical things like that where students have access to resources where they can be thinking through their ideas.  And then, yeah, I think just constantly affirming their ideas that, as a teacher, I think—I teach second grade this year and [they are] very different from the fourth graders that I student taught—but I think just knowing that every kid can do it. They are able, they have a lot in their mind. And I think affirming what you see and building their confidence does a lot for them. And so I think always being positive in what you see and starting with what you see them doing and not the mistakes or problems that are not important. Mike: Jenna, before we go, I wanted to ask you one final question. I wonder if you could talk about the resources that you drew on when you were developing the strategy showcase. Are there any particular recommendations you would have for someone who's listening to the podcast and wants to learn a little bit more about the practices or the foundations that would be important? Or anything else that you think it would be worth someone reading if they wanted to try to take up your ideas? Jenna: I know, in general, when we were developing this project—a lot of it again came from our seminar class that we did at UConn with Tutita—and we had a lot of great resources that she provided us. But I know one thing that we would see a lot that we referenced throughout our article is the National Council of Teachers of Mathematics. I think it's just really important that when you're building ideas to, one, look at research and projects that other people are doing to see connections that you can build on from your own classroom, and then also talking with your colleagues. A lot of this came from us talking and seeing what we saw in our classrooms and commonalities that we realized that we're in very different districts, we're in very different grades and what classrooms look like. Some of us were helping, pushing into a general ed classroom. Some of us were taking kids for small groups. But even across all those differences, there were so many similarities that we saw rooted in how kids approach problems or how kids thought about math. So I think also it's just really important to talk with the people that you work with and see how can you best support the students. And I think that was one really important thing for us, that collaboration along with the research that's already out there that people have done. Mike: Well, I think this is a good place to stop, but I just want to say thank you again. I really appreciate the way that you unpack the features of the strategy showcase, the way that you brought it to life in this interview. And I'm really hopeful that for folks who are listening, we've offered a spark and other people will start to take up some of the ideas and the features that you described. Thanks so much to all of you for joining us. It really has been a pleasure talking with all of you. Jenna: Thank you.  Anna: Thank you Mhret: Thank you.  Tutita: Thank you so much. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2025 The Math Learning Center | www.mathlearningcenter.org

I don't often have repeat guests on How To Fail but Mo Gawdat is the exception. When he first came on this podcast in 2019, he fundamentally changed my mindset and my approach to life. Back then, he was on a mission to make 1 billion people happier. Now, he returns to focus his brilliant philosophical and analytical brain to the perpetual human question: how to find true love, then nurture and sustain it. He joins me to discuss the three most frequent mistakes we make in love - and to explain how AI could be the saving of us. Mo is about to launch a game-changing AI-powered app called Emma that promises to help us all navigate the dating game with compassion and insight. This is the first time Mo has spoken in depth about this revolutionary new app so, yes, that IS a How To Fail exclusive, no biggie. ✨ IN THIS EPISODE: 00:00 Introduction 04:29 Personal Growth and Relationships 05:40 Heartbreak and Grief 10:03 Reflections on Love and Breakups 18:12 The Complexity of Modern Dating 21:45 Introducing Emma: The AI for True Love 29:53 The Mathematics of Dating 30:33 The Law of Large Numbers in Love 32:54 Dating Fatigue and Its Consequences 33:39 Game Theory in Relationships 36:52 AI's Role in Modern Relationships 39:15 The Economics of Love and Relationships 47:52 Finding Contentment Amidst Global Chaos

Renaissance Man Thomas Harriot was noted for many things - devising the theory of refraction, creating mathematical symbols including ‘greater than' and ‘lesser than', and being the first person to draw the Moon through a telescope. But the contribution for which he's most remembered is bringing back the potato to Britain - an event commonly credited to 3rd December, 1586. On first spotting the vegetable on Roanoke Island, he wrote: ‘They are a kind of roots of round form, some of the bigness of walnuts, some far greater, which are found in moist & marish grounds growing many together one by another in ropes, or as though they were fastened with a string. Being boiled or sodden they are very good meate.' In this episode, Arion, Olly and Rebecca ask what a ‘versifier' is; come up with a new name for Accountancy; and discover the bizarre means by which Antoine-Augustin Parmentier popularised spuds in France… Further Reading: • ‘The history of the potato: The humble vegetable that changed the world' (Sky HISTORY): https://www.history.co.uk/articles/the-history-of-the-potato-the-humble-vegetable-that-changed-the-world • ‘Thomas Harriot (1560 - 1621) - Biography' (MacTutor History of Mathematics, St Andrews University): https://mathshistory.st-andrews.ac.uk/Biographies/Harriot/ • ‘History through the eyes of the potato' (Leo Bear-McGuinness, TEDx 2015): https://www.youtube.com/watch?v=xROmDsULcLE This episode first aired in 2021 Love the show? Support us!  Join 

Rob riffs on the fifth studio album by No Doubt, “Rock Steady,” from December 2001 (Intro / Hella Good / Hey Baby / Platinum Blonde Life / Making Out). STAFF PICKS: “Blurry” by Puddle of Mudd — Lynch. “In Too Deep” by Sum 41 — Bruce.   ENTERTAINMENT TRACK: “A Kaleidoscope of Mathematics” (from the motion picture "A Beautiful Mind"). 

On today's episode, Kyle Grieve discusses powerful mental models from systems thinking and mathematics and applies them directly to investing and life. He breaks down concepts like feedback loops, kill criteria, scale, compounding, randomness, and regression to the mean to show how they shape real-world outcomes. He'll also share practical frameworks for improving decision-making, managing uncertainty, and positioning your portfolio to benefit from long-term compounding. IN THIS EPISODE YOU'LL LEARN: 00:00:00 - Intro 00:03:23 - How feedback loops stabilize or reinforce outcomes in investing 00:10:11 - How kill criteria help you make predetermined decisions in a noisy world 00:14:09 - Why the cone of uncertainty is useful for evaluating conviction and position sizing 00:17:33 - How scale changes the behavior, costs, and risks of a growing business 00:25:06 - How algorithms clarify which inputs drive the conclusions you rely on 00:30:20 - How to evaluate a company's ability to reach critical mass and become self-sustaining 00:35:35 - The hidden forms of compounding that are just as powerful as the visible ones 00:40:02 - Why power laws should influence your portfolio concentration 00:43:12 - How randomness shapes investing outcomes, and how to take advantage of it 00:51:24 - Why regression to the mean matters during periods of strong or weak performance Disclaimer: Slight discrepancies in the timestamps may occur due to podcast platform differences. BOOKS AND RESOURCES Join the exclusive ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠TIP Mastermind Community⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ to engage in meaningful stock investing discussions with Stig, Clay, Kyle, and the other community members. Buy Thinking in Systems ⁠here⁠. Buy The Great Mental Models Vol 3: Systems and Mathematics ⁠here⁠. Buy Quit ⁠here⁠. Listen to my interview with Annie Duke ⁠here⁠. Follow Kyle on ⁠⁠⁠X⁠⁠⁠ and ⁠⁠⁠LinkedIn⁠⁠⁠. Related ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠books⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ mentioned in the podcast. Ad-free episodes on our ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ ⁠⁠⁠⁠⁠⁠⁠⁠Premium Feed⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. NEW TO THE SHOW? Get smarter about valuing businesses in just a few minutes each week through our newsletter, ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠The Intrinsic Value Newsletter⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Check out our ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠We Study Billionaires Starter Packs⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Follow our official social media accounts: ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠X (Twitter)⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ | ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠LinkedIn⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ | ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Instagram⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ | ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Facebook⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ | ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠TikTok⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Browse through all our episodes (complete with transcripts) ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠here⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Try our tool for picking stock winners and managing our portfolios: ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠TIP Finance Tool⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Enjoy exclusive perks from our ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠favorite Apps and Services⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Learn how to better start, manage, and grow your business with the ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠best business podcasts⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. SPONSORS Support our free podcast by supporting our sponsors: Simple Mining Human Rights Foundation Unchained Onramp HardBlock Amazon Ads reMarkable Alexa+ Linkedin Talent Solutions Public.com Vanta Netsuite Shopify Abundant Mines Horizon Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://theinvestorspodcastnetwork.supportingcast.fm

In today's episode of Next Level University, hosts Kevin Palmieri and Alan Lazaros break down why so many people stay stuck by relying on emotion instead of objective data. You'll learn how understanding your numbers builds real confidence, how measurable feedback improves decision-making, and why tracking your behavior is a cornerstone of long-term personal development. This conversation highlights the role of data, clarity, and self-awareness in creating consistent results, especially for anyone serious about growth, success, and high performance. If you've been feeling uncertain, frustrated, or unclear about your next step, this episode reveals the skill that elevates focus, accuracy, and long-term progress. Press play and become the person who builds their future with intention and evidence, not emotion or chance.Learn more about:Next Level Hope Foundation – GoFundMe donation link https://gofund.me/5c6abcf7f Episode Reference:The Map of Mathematics - https://www.youtube.com/watch?v=OmJ-4B-mS-YVisual Asset:Foundational Mathematical Thinking - https://drive.google.com/file/d/1MVXeaS3F_7pK_aR3xHnQ7UGg-NPwbE31/view?usp=drive_link_______________________NLU is not just a podcast; it's a gateway to a wealth of resources designed to help you achieve your goals and dreams. From our Next Level Dreamliner to our Group Coaching, we offer a variety of tools and communities to support your personal development journey.For more information, check out our website and socials using the links below.

On October 16, 1843, William Rowan Hamilton was taking a walk with his wife Helen. He was on his way to preside over a meeting of the Royal Irish Academy. As Hamilton came to Broome Bridge, over the Royal Canal, the solution to a vexing problem finally emerged in front of him. He was so excited, and perhaps so afraid that he might forget, that he pulled out his penknife and carved the equation he had so suddenly conceived on the stonework of the bridge. That might not seem like such a revolutionary moment. But as my guest Robyn Arianrohd explains, Hamilton's equation was the result of long centuries of mathematical effort. And its consequences would be immense. Because Hamilton's thought made possible the concepts known as vectors and tensors. And vectors and tensors underlie much of modern science and technology, because they are used whenever a scientist or an engineer wants to use locations in space–everything from designing a bridge, to predicting the path of a gravitational wave; and there's quite a lot of territory in between those two applications. That moment by the Broome Bridge ushered in a new era. Robyn Arianrohd is a mathematician, and a historian of science. Her previous books include Thomas Harriot: A Life in Science, which she and I discussed in a conversation that was published on April 30, 2019. Her latest book is Vector: A Surprising Story of Space, Time, and Mathematical Transformation. For show notes, resources, and our archive, go the Historically Thinking Substack ChaptersThomas Harriet and the Birth of Modern AlgebraNavigation, Collisions, and Early Vector ConceptsNewton's Definition of Force and DirectionAugustus De Morgan and the Formalization of AlgebraHamilton's Breakthrough: Quaternions and Four DimensionsThe Non-Commutative RevolutionJames Clerk Maxwell and Electromagnetic TheoryMaxwell's Equations and the Nature of LightThe Vector Wars: Quaternions vs. VectorsTensors: Beyond Vectors to General RelativityThe Playful Seriousness of Mathematical DiscoveryConclusion: The Journey into History of Mathematics

What is the true structure of reality? In his fourth appearance on Mind-Body Solution, cognitive scientist Donald Hoffman returns with the most significant update yet to Conscious Realism: trace logic, decorated permutations, the emergence of spacetime from networks of conscious agents, and the strongest mathematical progress so far toward deriving Minkowski space from consciousness itself. Across nearly three hours, we explore what has changed in Hoffman's thinking since our last dialogue two years ago: breakthroughs in the trace-order formalism, new clarifications on evolution and perception, deeper implications for identity and suffering, and the surprising philosophical consequences of consciousness being fundamental. This is Hoffman at his most refined - technically rigorous, personally honest, and metaphysically bold.TIMESTAMPS:(00:00) — Intro(03:12) — What has changed in Hoffman's thinking in the last two years? (07:45) — Why Spacetime Is Doomed: The 2026 Case(12:58) — Conscious Agents: What's Changed in the New Theory(18:30) — Traces of Consciousness (2026): Don's Biggest Breakthrough Yet(25:44) — Restricted Channels of Consciousness (RCCs)(32:02) — The Mathematics of Trace Order & Trace Logic(38:55) — Is Reality Built from Relations, Not Things?(45:40) — What the Spacetime Headset Really Is(52:18) — Scattering Amplitudes & the Illusion of Objects(59:50) — Why Evolution Hides the Truth (Updated Evidence)(1:07:14) — Perception as a User Interface, Not a Window on Reality(1:14:32) — Are Particles Just Icons? The Physics Implications(1:22:10) — Causality, Emergence, Time & the √n Structure of Trace Chains(1:29:48) — Can We Test Conscious Realism in the Lab?(1:37:05) — AI, Conscious Agents & Synthetic Phenomena(1:45:22) — Conscious Realism vs Idealism, Physicalism & Competing Frameworks(1:53:44) — The Meaning Question: Why Is There Something It's Like?(2:02:58) — What This Theory Says About Death & Identity(2:10:00) – Identity, the Avatar, Death, Suffering & the “Infinite Self” (2:30:00) – Meditation & Waking Up from the Headset (2:40:00) – The New Paper Timeline & Call for Collaborators (2:48:00) – Closing reflectionsEPISODE LINKS:- Donald's Website: https://www.cogsci.uci.edu/~ddhoff/- Donald's Books: https://tinyurl.com/5x7bmzbd- Donald's Publications: https://tinyurl.com/bp7btw9a- Donald's Round 1: https://youtu.be/M5Hz1giUUT8- Donald's Round 2: https://youtu.be/Toq9YLl49KM- Donald's Round 3: https://youtu.be/QRa8r5xOaAA- Donald's Lecture 1: https://youtu.be/r_UFm8GbSvU- Donald's Lecture 2: https://youtu.be/YBmzqNIlbcICONNECT:- Website: https://mindbodysolution.org - YouTube: https://youtube.com/@MindBodySolution- Podcast: https://creators.spotify.com/pod/show/mindbodysolution- Twitter: https://twitter.com/drtevinnaidu- Facebook: https://facebook.com/drtevinnaidu - Instagram: https://instagram.com/drtevinnaidu- LinkedIn: https://linkedin.com/in/drtevinnaidu- Website: https://tevinnaidu.com=============================Disclaimer: The information provided on this channel is for educational purposes only. The content is shared in the spirit of open discourse and does not constitute, nor does it substitute, professional or medical advice. We do not accept any liability for any loss or damage incurred from you acting or not acting as a result of listening/watching any of our contents. You acknowledge that you use the information provided at your own risk. Listeners/viewers are advised to conduct their own research and consult with their own experts in the respective fields.

Machine learning using neural networks has led to a remarkable leap forward in artificial intelligence, and the technological and social ramifications have been discussed at great length. To understand the origin and nature of this progress, it is useful to dig at least a little bit into the mathematical and algorithmic structures underlying these techniques. Anil Ananthaswamy takes up this challenge in his book Why Machines Learn: The Elegant Math Behind Modern AI. In this conversation we give a brief overview of some of the basic ideas, including the curse of dimensionality, backpropagation, transformer architectures, and more.Blog post with transcript: https://www.preposterousuniverse.com/podcast/2025/11/24/336-anil-ananthaswamy-on-the-mathematics-of-neural-nets-and-ai/Support Mindscape on Patreon.Anil Ananthaswamy received a Masters degree in electrical engineering from the University of Washington, Seattle. He is currently a freelance science writer and feature editor for PNAS Front Matter. He was formerly the deputy news editor for New Scientist, a Knight Science Journalism Fellow at MIT, and journalist-in-residence at the Simon Institute for the Theory of Computing, University of California, Berkeley. He organizes an annual science journalism workshop at the National Centre for Biological Sciences at Bengaluru, India.Web siteAmazon author pageWikipediaSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

Bob revisits capital and interest theory to show why the textbook result “interest = MPK” only holds in a one-good world, and why in actual markets the interest rate emerges from time, prices, and capital valuation—not raw productivity.Bob and Alberto Bisin Discuss the Use of Mathematics in Economics: Mises.org/HAP527aBob's Dissertation, "Unanticipated Intertemporal Change in Theories of Interest": Mises.org/HAP527bThe Mises Institute is giving away 100,000 copies of Hayek for the 21st Century. Get your free copy at Mises.org/HAPodFree

Episode: 1475 The tragic tale of Evariste Galois.  Today, let's tell the remarkable tale of Evariste Galois.

After 27 years, Melvyn Bragg has decided to step down from the In Our Time presenter's chair. With over a thousand episodes to choose from, he has selected just six that capture the huge range and depth of the subjects he and his experts have tackled. In this third of his choices, we hear Melvyn Bragg and his guests discuss Greek philosophy. Their topic is Zeno of Elea, a pre-Socratic philosopher from c490-430 BC whose paradoxes were described by Bertrand Russell as "immeasurably subtle and profound." The best known argue against motion, such as that of an arrow in flight which is at a series of different points but moving at none of them, or that of Achilles who, despite being the faster runner, will never catch up with a tortoise with a head start. Aristotle and Aquinas engaged with these, as did Russell, yet it is still debatable whether Zeno's Paradoxes have been resolved. With Marcus du Sautoy Professor of Mathematics and Simonyi Professor for the Public Understanding of Science at the University of Oxford Barbara Sattler Lecturer in Philosophy at the University of St Andrews and James Warren Reader in Ancient Philosophy at the University of Cambridge Producer: Simon Tillotson In Our Time is a BBC Studios Production Spanning history, religion, culture, science and philosophy, In Our Time from BBC Radio 4 is essential listening for the intellectually curious. In each episode, host Melvyn Bragg and expert guests explore the characters, events and discoveries that have shaped our world

From Rakim to Kendrick Lamar, this is the story of hip-hop's obsession with numbers. Dissect's Cole Cuchna breaks down the evolution of “number bars” - a lyrical tradition where rappers use math, numeric sequences, and wordplay to showcase technical skill and encode hidden meaning. Beginning with Rakim's groundbreaking verse on “My Melody” (1986) - a quatrain built around groups of seven that secretly mirrors his own 21-letter name - we trace how MCs have used numbers as both a mathematical signature and a symbolic device for decades. From Melle Mel's divine 7-count in “Superrappin” to Jay-Z's “22 Twos”, Biggie's “Ten Crack Commandments,” and Mos Def's “Mathematics,” numbers became an essential part of hip hop tradition and lyricism. By the 2000s, artists like Lupe Fiasco, J. Cole, JID, Vince Staples, and Kendrick Lamar transformed number schemes into complex storytelling tools. We unpack everything from Lupe's hidden 3–2–1 countdown on Kanye West's “Touch the Sky” to Kendrick's quantum-level equations on “Nosetalgia.” Learn more about your ad choices. Visit podcastchoices.com/adchoices

What happens when a government abruptly cuts off the lifeline of pure science? Imagine canceling Albert Einstein just before he published [E = mc². Terence Tao, the “Mozart of Mathematics,” was one of the unlucky researchers hit when the Trump administration suddenly terminated his federal research funding. Today, I walk and talk with Tao at UCLA to understand how America's greatest living mathematician found himself blindsided by a bureaucratic earthquake — and what it means for the future of discovery. This is Part 1 of our deep dive into Tao's work, his warnings about the collapse of U.S. research infrastructure, and why mathematics is the unseen root system supporting all of modern technology.

This week on Schauer Thoughts we have a special guest - please give a warm welcome to Mina Neuberg, CEO of WonderMath! Also, this episode is NOT an ad, I am not being paid, I just really love math and wanted to discuss learning and executive functioning with the executive putting the “fun” in functional learning. No but seriously, math is incredibly important and I appreciate y'all listening and *hopefully* expanding the communal comfort zone! Learn More About WonderMath: https://www.wondermath.com/  Where to Reach Mina: mina@wondermath.com  New Book Club Information: https://www.patreon.com/posts/new-book-for-143088045  Resources: What We Value: The Neuroscience of Choice & Change - Emily Falk The Power of Fun - Catherine Price Mathematics for Human Flourishing - Francis Su Is Math Real? - Eugenia Cheng  The Knowledge Illusion: Why We Never Think Alone - Philip Fernbach  Neural correlates of hate https://pubmed.ncbi.nlm.nih.gov/18958169/ What Is Hate and Where Does It Live in the Brain? https://www.psychologytoday.com/us/blog/your-brain-on-food/202208/what-is-hate-and-where-does-it-live-in-the-brain The premotor cortex https://www.physio-pedia.com/Premotor_Cortex#:~:text=The%20premotor%20cortex%20is%20a,of%20the%20contralateral%20hemisphere%20alone. Behavioral energetics in human locomotion: how energy use influences how we move https://pmc.ncbi.nlm.nih.gov/articles/PMC11993254/  Demonstration and Pantomime in the Evolution of Teaching https://pmc.ncbi.nlm.nih.gov/articles/PMC5361109/ Total Physical Response (TPR) - Teaching Method https://www.researchgate.net/publication/392376539_Total_Physical_Response_TPR Screen Apnea  https://www.npr.org/2024/06/10/1247296780/screen-apnea-why-screens-cause-shallow-breathing  Olfactory Enrichment to Improve Memory https://pmc.ncbi.nlm.nih.gov/articles/PMC10405466/ What the Thalamus Does https://teachersinstitute.yale.edu/curriculum/units/2012/3/12.03.02/4#:~:text=In%20this%20way%2C%20the%20thalamus%20is%20screening,matters%20of%20value%20and%20filtering%20out%20distractions.  This is How the Brain Filters Out Unimportant Details https://www.psychologytoday.com/us/blog/brain-babble/201502/is-how-the-brain-filters-out-unimportant-details#:~:text=This%20%E2%80%9Creciprocal%E2%80%9D%20connectivity%20can%20be,popcorn%2C%20and%20air%20conditioning). Movement-Based Learning: Students Need to Use Their Bodies to Learn  https://www.teachhub.com/teaching-strategies/2025/03/movement-based-learning-students-need-to-use-their-bodies-to-learn/  Math Has Its Own Language. How Can Students Learn to Speak It? https://www.edweek.org/teaching-learning/math-has-its-own-language-how-can-students-learn-to-speak-it/2024/09 Conceived linearities in mathematics education and how to disrupt them https://www.tandfonline.com/doi/full/10.1080/14794802.2025.2579307?src=#d1e125 How Did You Solve It? Metacognition in Mathematics  https://www.ascd.org/el/articles/how-did-you-solve-it-metacognition-in-mathematics Writing Problems in Possessive Form https://www.ef.edu/english-resources/english-grammar/forming-possessive/ Learn more about your ad choices. Visit podcastchoices.com/adchoices