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// GUEST //X: https://x.com/romanyamWebsite: https://faculty.cse.louisville.edu/roman/index.html// SPONSORS //Heart and Soil Supplements (use discount code BREEDLOVE): https://heartandsoil.co/Blockware Solutions: https://mining.blockwaresolutions.com/breedloveOnramp: https://onrampbitcoin.com/?grsf=breedlovePerformance Lab Supplements: https://www.performancelab.com/breedloveThe Farm at Okefenokee: https://okefarm.com/Club Orange: https://www.cluborange.org/Efani — Protect Yourself From SIM Swaps: https://www.efani.com/breedlove // PRODUCTS I ENDORSE //Protect your mobile phone from SIM swap attacks: https://www.efani.com/breedloveLineage Provisions (use discount code BREEDLOVE): https://lineageprovisions.com/?ref=breedlove_22Colorado Craft Beef (use discount code BREEDLOVE): https://coloradocraftbeef.com/Salt of the Earth Electrolytes: http://drinksote.com/breedloveJawzrsize (code RobertBreedlove for 20% off): https://jawzrsize.com// UNLOCK THE WISDOM OF THE WORLD'S BEST NON-FICTION BOOKS //https://course.breedlove.io/ // SUBSCRIBE TO THE CLIPS CHANNEL //https://www.youtube.com/@robertbreedloveclips2996/videos // TIMESTAMPS //0:00 – WiM Episode Trailer1:37 – Entering the Geometry of Reality18:42 – Consciousness, Pattern & Intelligence42:11 – Mathematics as a Universal Language53:26 – Heart and Soil Supplements54:26 – Mine Bitcoin with Blockware Solutions56:02 – Sacred Geometry & Ancient Knowledge1:22:18 – AI, Meaning & Symbolic Recognition1:49:22 – Onramp Bitcoin Custody1:50:20 – Performance Lab Supplements1:52:04 – Can AI Understand Truth?2:28:41 – Intelligence vs Consciousness3:06:40 – The Farm at Okefenokee3:08:02 – Civilization Cycles & Lost Knowledge3:47:19 – The Limits of Computation4:29:39 – Club Orange4:31:02 – Human Creativity vs Machine Intelligence5:17:49 – Efani: Protect Yourself From SIM Swaps5:18:56 – Unlock the Wisdom of the Best Non-Fiction Books5:19:58 – Outro // PODCAST //Podcast Website: https://whatismoneypodcast.com/Apple Podcast: https://podcasts.apple.com/us/podcast/the-what-is-money-show/id1541404400Spotify: https://open.spotify.com/show/25LPvm8EewBGyfQQ1abIsERSS Feed: https://feeds.simplecast.com/MLdpYXYI // SUPPORT THIS CHANNEL //Bitcoin: 3D1gfxKZKMtfWaD1bkwiR6JsDzu6e9bZQ7Sats via Strike: https://strike.me/breedlove22Paypal: https://www.paypal.com/paypalme/RBreedloveVenmo: https://account.venmo.com/u/Robert-Breedlove-2 // SOCIAL //Breedlove X: https://x.com/Breedlove22WiM? X: https://x.com/WhatisMoneyShowLinkedin: https://www.linkedin.com/in/breedlove22/Instagram: https://www.instagram.com/breedlove_22/TikTok: https://www.tiktok.com/@breedlove22Substack: https://breedlove22.substack.com/All My Current Work: https://linktr.ee/robertbreedlove
What's scarier than ghosts? MATH! This week we're diving into the horror of math, algorithms, and the unsettling idea that randomness might not be random at all. From the Princeton PEAR Experiment (where intention may have bent probability) to dating apps, advertising algorithms, and the numbers quietly running our lives.
Podcast SEO and monetization strategies tailored for local businesses is today's episode discussion. Favour Obasi-ike emphasizes the importance of metadata, noting that elements like podcast titles, descriptions, and author names serve as critical search signals for discovery.By treats these fields as structured data, creators can establish local authority and ensure their content surfaces in specific user queries across platforms like Spotify and Apple Podcasts.The source further highlights the compounding value of backlinking, explaining how consistent episode releases create a vast network of searchable links that drive traffic back to a brand's website. Ultimately, the text argues that a well-optimized podcast acts as a long-term intellectual property asset that builds credibility and solves audience problems through searchable, evergreen audio content.In the 2026 search ecosystem, local visibility is no longer a matter of chance; it is a matter of engineering. This episode serves as a strategic blueprint for local businesses to command "page dominance" by transforming audio content into a high-authority digital asset. By deploying a "spread map" strategy—scaling influence from local roots to international authority—business owners can ensure their brand is the definitive answer to specific consumer queries.The objective is to move beyond the "hobbyist" mindset and treat podcasting as a capital-efficient SEO machine. We explore how to build an "engine" that runs independently via technical metadata and RSS syndication, allowing your brand to reside permanently in the search database.Key Takeaways for Local Business Owners1. Metadata is Your Search ID: Your title, author field, and description must match the exact phrases your customers use. If your "ID" doesn't match the search query, the algorithm cannot process your "legal documents," and your business remains invisible.2. Exploit the 50x50 Rule: Syndication is a volume game. By appearing on 50 platforms, you create thousands of high-authority backlinks. This sheer volume of structured data makes your brand unavoidable in local searches.3. Implementation over Information: ROI is the result of action, not note-taking. Podcasting is a long-term index fund for your brand; the earlier you start the "audio documentation," the more interest your digital legacy accrues. Move from "doer" to "architect" today.Need to Book An Appointment?>> Book a Complimentary SEO Discovery Call with Favour Obasi-Ike>> Visit Work and PLAY Entertainment website to learn about our digital marketing services>> Join our exclusive SEO Marketing community>> Read SEO Articles>> Subscribe to the We Don't PLAY Podcast>> Purchase Flaev Beatz Beats OnlinePodcast Timestamps[00:00:00] – The Spread Map: Establishing the strategic journey from local business to international brand authority.[00:03:00] – Statistical Authority: Reviewing personal benchmarks (600 episodes, 156 countries) as a model for growth.[00:06:00] – The Harry Potter Paradox: Why naming your show for the "benefit" is the only way to be found before you are famous.[00:10:00] – The Psychology of Blue Links: Why "Blue Links" signify trust and confidence in the search results.[00:14:00] – Spotify Signal Case Study: Using the phrase "workout habits for men over 40" to identify exact-match search signals.[00:22:00] – Compounding Link Math: The 50x50 breakdown of how to generate 2,500 links across platforms like SiriusXM and iHeart.[00:31:00] – The Celese Interaction: Overcoming ADHD and task-paralysis by choosing documentation over perfection.[00:45:00] – The Legacy Challenge: Transitioning from a task-based worker to a legacy-based brand architect.The Mathematics of Syndication & The "Compounding Effect"Strategic dominance is a function of Depth and Cadence. While frequency is important, "Depth" is determined by your average episode length. A 60-minute episode provides sixty times more data points for an algorithm to index than a one-minute clip.The true ROI of podcasting is found in the Compounding Link Formula:50 Episodes (One year of weekly audio documentation) x 50 Distribution Platforms (Apple, Spotify, SiriusXM, Podchaser, Castbox, iHeart, etc.) = 2,500 High-Authority BacklinksThis volume creates a "digital balloon that never pops." As you add more helium (content), the structure becomes stiffer and more secure. To maximize this, maintain a Cadence (release cycle) closer to "1" (daily). A faster cadence spins the RSS feed more frequently, signaling to search engines that your brand is an active, relevant authority.The following 15 monetization levers are the tactical parameters required to convert conversational documentation into long-term ROI and a lasting digital legacy.Episode Breakdown on the 15 Monetization StrategiesPART 1: CORE DISCOVERY METADATA (Your Digital ID Card)1. Podcast TitleExecution: Match the show name to the specific topic or core benefit your audience seeks.So What? Listeners search for solutions and interests, not your name. A descriptive title ensures discoverability in search before you have a famous brand.2. Podcast DescriptionExecution: Exploit the full ~4,000-character limit as a "Search Bank." Use refined keywords, clear value propositions, and a strong call-to-action.So What? This is your show's primary Search ID. If it doesn't match user queries, algorithms can't "read" or rank your content effectively.3. Author/Host FieldExecution: Strategically expand your name with professional identifiers (e.g., "Alex Chen | Venture Capital Analyst").So What? This data feeds APIs and LLMs, establishing your niche authority within recommendation systems and digital assistants.4. Genre & Category SelectionExecution: Use platform hierarchies (e.g., ListenNotes, Apple) to select precise Primary, Secondary, and Tertiary categories.So What? Correct categorization moves you from competing with millions of general shows to dominating a specific, interested listener ecosystem.5. Episode TitleExecution: Adopt a clear, "Guest-First" or "Topic-First" naming convention (e.g., "Dr. Sarah Lee: The Neuroscience of Sleep").So What? It maximizes clarity for listeners and SEO. A guest's name at the front captures their audience and amplifies "link juice" to that episode URL.6. Episode DescriptionExecution: Implement web-style formatting: use H2/H3 headers, bullet points, timestamps, and hyperlinks to key resources.So What? Structured data helps both listeners scan and bots "dissect" your content, boosting engagement metrics and canonical linking power.PART 2: VISUAL & TECHNICAL EXECUTION7. Podcast Cover ArtExecution: Command professionalism with compliant, 3000 x 3000 pixels, visually simple art that is legible at thumbnail size.So What? High-quality, optimized art provides an immediate competitive edge against the significant portion of shows using amateur visuals.8. Episode Cover Art (Optional but Powerful)Execution: For key interviews, create guest-centric visuals that differ from your main show art.So What? Visual differentiation in a subscriber's feed signals unique, fresh value, increasing click-through rates for specific high-interest topics.9. Ad Roll PlacementsExecution: Strategically engineer ad breaks: pre-roll (for direct response), mid-roll (for highest attention), post-roll (for brand storytelling).So What? These are primary monetization vehicles. Placement affects listener retention and ad performance by capturing attention at different psychological stages.10. RSS Feed ManagementExecution: Balance your public RSS feed with private, gated feeds (via platforms like Hello Audio or Supercast) for bonus or premium content.So What? Private feeds enable direct community monetization and foster loyalty by delivering exclusive, "trust-based" content to high-value subscribers.PART 3: DISTRIBUTION & AMPLIFICATION11. Email & Affiliate LeverageExecution: Use automated tools to turn podcast transcripts into newsletter content that drives traffic to affiliate offers or key resources.So What? This captures high-intent listeners where they live (their inbox), converting passive listening into measurable action.12. Social Media DistributionExecution: Systematically cross-post short, thematic audio clips (with captions and video) to platforms like LinkedIn and Instagram.So What? It transforms one hour of recording into weeks of "top-of-funnel" awareness, building connection volume and attracting new audiences.13. Backlink GenerationExecution: Understand that every major hosting platform (Spotify, Apple) creates a backlink to your website from your show profile.So What? This generates vital "link juice" from high-authority domains, strengthening your primary website's search engine ranking.14. Website Integration & AnalyticsExecution: Host a dedicated podcast page on your site and connect it to Google Search Console.So What? This allows you to track how people find and interact with your podcast via search, providing data to refine your topic and keyword strategy.15. Sonic Branding (Musical Intelligence)Execution: Deploy a distinct instrumental theme for each season or series.So What? A fresh sonic identity signals a new "era" or focus for your show, boosting production value and maintaining listener retention through auditory novelty.See Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.
This episode of Room to Grow, Curtis and Joanie discuss two publications they have engaged with regarding technology, adolescents, and learning. The Anxious Generation describes the impact of smart phones and other recent technologies on childhood development, providing an understanding of what is happening internally for students in our classrooms. The Disengaged Teen utilizes research data around modes of learning and how they play out in terms of classroom behaviors. Our hosts make connections between these texts and what these ideas mean for math educators and classroom practices. Additional referenced content includes:· Book: The Anxious Generation by Jonathan Haidt· Podcast with Trevor Noah and Jonathan Haidt· Book: The Disengaged Teen by Rebecca Winthrop and Jenny AndersonDid 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.
Episode: 2550 Could Napoleon have proved Napoleon's Theorem? Today, did he, or didn't he?
This Blind Abilities episode shines a spotlight on internships for blind and low-vision students—and why starting early can open real doors. Tou Yang and Randi Lasher from State Services for the Blind of Minnesota (SSB), break down how high school and college students can access paid and unpaid internships that build skills, confidence, and career momentum. Listeners learn what internships really are, why they matter beyond just a paycheck, and how they connect classroom learning to real-world experience. The conversation highlights how SSB helps students explore careers, prepare for post-secondary education, advocate for themselves, and find meaningful internship opportunities across Minnesota. From local city programs to statewide options in technology, healthcare, STEM, public service, and more, this episode makes one thing clear: opportunities exist—but timing matters. Whether you're planning for summer, next year, or your future career path, this episode gives students practical guidance, resources, and motivation to take action and get ahead. Links to Internship Opportunities mentioned in this episode: Handshake - Summer Internships for College Students · Step Up - Kick Start Your Career with Step Up (Minneapolis) · Right Start - Youth Jobs Internships (St. Paul) · Genisis Works - Where Tomorrow's Work Force Begins · Urban Scholars - Internships and Training · Scrubs Camp - Medical Careers · Seeds Student Worker Program · Phoenix Student Worker Program - Science, Technology, engineering or Mathematics · State of Minnesota Careers Interns and Student Workers · BrookLynk- Summer Student Internship Program (Brooklyn Center, Brooklyn Park) · Tree Trust Summer Students Internships · Three Rivers Park Internship Program · The Brand lab - Marketing and Graphic Design Program · the Minnesota Historical Society - Work in a Museum! · SSB Youth Services Work Based Learning and Work Readiness opportunities · Career Force Locations in Minnesota To find out more about the services provided at State Services for the Blind, and what they can do for you, contact Shane DeSantis at shane.desantis@state.mn.us or call Shane at 651-385-5205. Full Transcript Thanks for listening!
The widespread adoption of and the rapid evolution of generative AI platforms have created substantial challenges for faculty in how we assess student learning. In this episode, Lew Ludwig and Todd Zakrajsek join us to discuss a new resource they have created that is designed to help faculty use AI to efficiently support teaching practices based on the science of learning. Lew is a Professor of Mathematics at Denison University, where he served as Director of the Center for Learning and Teaching from 2020 to 2025. Much of his recent work has focused on innovative methods for utilizing generative AI. Todd is an Adjunct Associate Research Professor at the University of North Carolina at Chapel Hill, from which he just retired a few months ago after 17 years. He is also the Director of the International Teaching Learning Cooperative and the Director of four Lilly conferences on evidence-based teaching and learning. Todd is the author of many superb books, and has published six books (so far) in the past five years. A transcript of this episode and show notes may be found at http://teaforteaching.com.
In this episode, Dean returns to the host's chair to welcome back Maegan and Kyle for the second half of their "Behind the Books" conversation, shifting the focus from the writing process to the messy reality of the classroom. Together, they contrast their unique creative styles from Kyle's "procrastination-to-panic" sprint to Maegan's marathon of task testing and open up about the vulnerability required to publish a static resource in an ever-evolving educational landscape. They discuss the feedback they have received and explore how teaching with intention can help alleviate math trauma. The conversation also dives into the power of storytelling to keep students engaged during dry curricular units, ensuring math acts as both a mirror and a window for learners, before concluding with reflections on how student solutions often surprised both and why the ultimate goal is teaching students that life, unlike a textbook answer key, is often "messy and gray."Links:Building Thinking Classrooms Tasks in Mathematics, Grades K-5Building Thinking Classrooms Tasks in Mathematics, Grades 6-12Saskatchewan Understand Math Conference 2026
Welcome to The Game w/Alex Hormozi, hosted by entrepreneur, founder, investor, author, public speaker, and content creator Alex Hormozi. On this podcast, you'll hear how to get more customers, make more profit per customer, how to keep them longer, and the many failures and lessons Alex has learned and will learn on his path from $100M to $1B in net worth.Wanna scale your business? Click here.Follow Alex Hormozi's Socials:LinkedIn | Instagram | Facebook | YouTube | Twitter | Acquisition
1 Samuel 30: God does not give based on our merit; God gives based on His grace. We are to follow His generosity with our own.
Delivered on October 8, 2025 at the Istituto Lombardo Accademia di Scienze e Lettere in Milan, Italy as part of their Leonardo da Vinci lecture series.
Episode117-Asale Smith, "Creating a Space Where Confidence in Mathematics Grows"
The Science History Podcast, now in its 9th year, has spanned Trump's first term in office, four years of the Biden Administration, and a year of the second Trump Administration, not to mention a global pandemic, horrific wars around the world, and the emergence of AI. So now seems like the perfect moment for some levity. The master of musical satire, Tom Lehrer, passed away in 2025. Here is my celebration of Lehrer's ability to make us laugh during the even more tumultuous times of the Civil Rights era, the Vietnam War, the Cold War, and political assassinations and violent polarization.
This is a recap of the top 10 posts on Hacker News on January 09, 2026. This podcast was generated by wondercraft.ai (00:30): Anthropic blocks third-party use of Claude Code subscriptionsOriginal post: https://news.ycombinator.com/item?id=46549823&utm_source=wondercraft_ai(01:50): The Vietnam government has banned rooted phones from using any banking appOriginal post: https://news.ycombinator.com/item?id=46555963&utm_source=wondercraft_ai(03:10): Cloudflare CEO on the Italy finesOriginal post: https://news.ycombinator.com/item?id=46555760&utm_source=wondercraft_ai(04:30): Show HN: I made a memory game to teach you to play piano by earOriginal post: https://news.ycombinator.com/item?id=46556210&utm_source=wondercraft_ai(05:50): European Commission issues call for evidence on open sourceOriginal post: https://news.ycombinator.com/item?id=46550912&utm_source=wondercraft_ai(07:10): Mathematics for Computer Science (2018) [pdf]Original post: https://news.ycombinator.com/item?id=46550895&utm_source=wondercraft_ai(08:31): Kagi releases alpha version of Orion for LinuxOriginal post: https://news.ycombinator.com/item?id=46553343&utm_source=wondercraft_ai(09:51): Flock Hardcoded the Password for America's Surveillance Infrastructure 53 TimesOriginal post: https://news.ycombinator.com/item?id=46555807&utm_source=wondercraft_ai(11:11): “Erdos problem #728 was solved more or less autonomously by AI”Original post: https://news.ycombinator.com/item?id=46560445&utm_source=wondercraft_ai(12:31): What happened to WebAssemblyOriginal post: https://news.ycombinator.com/item?id=46551044&utm_source=wondercraft_aiThis is a third-party project, independent from HN and YC. Text and audio generated using AI, by wondercraft.ai. Create your own studio quality podcast with text as the only input in seconds at app.wondercraft.ai. Issues or feedback? We'd love to hear from you: team@wondercraft.ai
// GUEST //Website: https://robertedwardgrant.com/Youtube: https://www.youtube.com/@Robert_Edward_Grant/videos // SPONSORS //Heart and Soil Supplements (use discount code BREEDLOVE): https://heartandsoil.co/Blockware Solutions: https://mining.blockwaresolutions.com/breedloveOnramp: https://onrampbitcoin.com/?grsf=breedlovePerformance Lab Supplements: https://www.performancelab.com/breedloveThe Farm at Okefenokee: https://okefarm.com/Club Orange: https://www.cluborange.org/Efani — Protect Yourself From SIM Swaps: https://www.efani.com/breedlove // PRODUCTS I ENDORSE //Protect your mobile phone from SIM swap attacks: https://www.efani.com/breedloveLineage Provisions (use discount code BREEDLOVE): https://lineageprovisions.com/?ref=breedlove_22Colorado Craft Beef (use discount code BREEDLOVE): https://coloradocraftbeef.com/Salt of the Earth Electrolytes: http://drinksote.com/breedloveJawzrsize (code RobertBreedlove for 20% off): https://jawzrsize.com// UNLOCK THE WISDOM OF THE WORLD'S BEST NON-FICTION BOOKS //https://course.breedlove.io/ // SUBSCRIBE TO THE CLIPS CHANNEL //https://www.youtube.com/@robertbreedloveclips2996/videos // TIMESTAMPS //0:00 – WiM Episode Trailer1:37 – Entering the Geometry of Reality18:42 – Consciousness, Pattern & Intelligence42:11 – Mathematics as a Universal Language53:26 – Heart and Soil Supplements54:26 – Mine Bitcoin with Blockware Solutions56:02 – Sacred Geometry & Ancient Knowledge1:22:18 – AI, Meaning & Symbolic Recognition1:49:22 – Onramp Bitcoin Custody1:50:20 – Performance Lab Supplements1:52:04 – Can AI Understand Truth?2:28:41 – Intelligence vs Consciousness3:06:40 – The Farm at Okefenokee3:08:02 – Civilization Cycles & Lost Knowledge3:47:19 – The Limits of Computation4:29:39 – Club Orange4:31:02 – Human Creativity vs Machine Intelligence5:17:49 – Efani: Protect Yourself From SIM Swaps5:18:56 – Unlock the Wisdom of the Best Non-Fiction Books5:19:58 – Outro // PODCAST //Podcast Website: https://whatismoneypodcast.com/Apple Podcast: https://podcasts.apple.com/us/podcast/the-what-is-money-show/id1541404400Spotify: https://open.spotify.com/show/25LPvm8EewBGyfQQ1abIsERSS Feed: https://feeds.simplecast.com/MLdpYXYI // SUPPORT THIS CHANNEL //Bitcoin: 3D1gfxKZKMtfWaD1bkwiR6JsDzu6e9bZQ7Sats via Strike: https://strike.me/breedlove22Paypal: https://www.paypal.com/paypalme/RBreedloveVenmo: https://account.venmo.com/u/Robert-Breedlove-2 // SOCIAL //Breedlove X: https://x.com/Breedlove22WiM? X: https://x.com/WhatisMoneyShowLinkedin: https://www.linkedin.com/in/breedlove22/Instagram: https://www.instagram.com/breedlove_22/TikTok: https://www.tiktok.com/@breedlove22Substack: https://breedlove22.substack.com/All My Current Work: https://linktr.ee/robertbreedlove
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
Learning to teach math teachers better with with Dr. Amber Candela, Associate Professor at the University of Missouri-St. Louis, as she shares her advice and expertise on being a mathematics teacher educator and her role as one of the three co-editors of the Mathematics Teacher Educator Journal, a joint venture between the Association of Mathematics Teacher Educators and the National Council of Teachers of Mathematics. Links from the episode Mathematics Teacher Educator Journal (https://pubs.nctm.org/view/journals/mte/mte-overview.xml) Write for the Mathematics Teacher Educator Journal (https://www.nctm.org/Publications/write-review-referee/journals/Write-for-Mathematics-Teacher-Educator/) Review for the Mathematics Teacher Educator Journal (https://www.nctm.org/Publications/write-review-referee/journals/Review-for-Mathematics-Teacher-Educator/) Practice-Driven Professional Development (PDPD) https://practicedrivenpd.com/ Otten, S., de Araujo, Z., & Candela, A. G. (2025). The Benefits of Modesty: Considering Incremental Professional Development for Mathematics Teachers. Education Sciences, 15(4), 473. https://doi.org/10.3390/educsci15040473 Making Sense of Mathematics for Teaching to Inform Instructional Quality (Applying the TQE Process in Teachers' Math Strategies) (https://www.solutiontree.com/making-sense-of-math-teaching-to-inform-instructional-quality.html) Special Guest: Amber Candela.
Empowered Relationship Podcast: Your Relationship Resource And Guide
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
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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
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
Know Your Risk Radio with Zach Abraham, Chief Investment Officer, Bulwark Capital Management
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.
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.
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
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
Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
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.
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
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