Podcasts about Mathematics

Episode: 1379 Frank and Peter Griffin: teaching calculus.  Today, an obituary brings back memories.

Head on over to https://cell.ver.so/TOE and use coupon code TOE at checkout to save 15% on your first order. Get ready to witness a turning point in mathematical history: in this episode, we dive into the AI breakthroughs that stunned number theorists worldwide. Join us as Professor Yang-Hue Hi discusses the murmuration conjecture, shows how DeepMind, OpenAI, and EpochAI are rewriting the rules of pure math, and reveals what happens when machines start making research-level discoveries faster than any human could. AI is taking us beyond proof straight into the future of discovery. As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe Join My New Substack (Personal Writings): https://curtjaimungal.substack.com Listen on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e Timestamps: 00:00 Introduction to a New Paradigm 01:34 The Changing Landscape of Research 03:30 Categories of Machine Learning in Mathematics 06:53 Researchers: Birds vs. Hedgehogs 09:36 Personal Experiences with AI in Research 11:44 The Future Role of Academics 14:08 Presentation on the AI Mathematician 16:14 The Role of Intuition in Discovery 18:00 AI's Assistance in Vague Problem Solving 18:48 Newton and AI: A Historical Perspective 20:59 Literature Processing with AI 24:34 Acknowledging Modern Mathematicians 26:54 The Influence of Data on Mathematical Discovery 30:22 The Riemann Hypothesis and Its Implications 31:55 The BST Conjecture and Data Evolution 33:29 Collaborations and AI Limitations 36:04 The Future of Mathematics and AI 38:31 Image Processing and Mathematical Intuition 41:57 Visual Thinking in Mathematics 49:24 AI-Assisted Discovery in Mathematics 51:34 The Murmuration Conjecture and AI Interaction 57:05 Hierarchies of Difficulty 58:43 The Memoration Breakthrough 1:00:28 Understanding the BSD Conjecture 1:01:45 Diophantine Equations Explained 1:03:39 The Cubic Complexity 1:19:03 Neural Networks and Predictions 1:21:36 Breaking the Birch Test 1:24:44 The BSD Conjecture Clarified 1:26:21 The Role of AI in Discovery 1:30:29 The Memoration Phenomenon 1:32:59 PCA Analysis Insights 1:35:50 The Emergence of Memoration 1:38:35 Conjectures and AI's Role 1:41:29 Generalizing Biases in Mathematics 1:44:55 The Future of AI in Mathematics 1:49:28 The Brave New World of Discovery Links Mentioned: - Topology and Physics (book): https://amzn.to/3ZoneEn - Machine Learning in Pure Mathematics and Theoretical Physics (book): https://amzn.to/4k8SXC6 - The Calabi-Yau Landscape (book): https://amzn.to/43DO7H0 - Yang-Hui's bio and published papers: https://www.researchgate.net/profile/Yang-Hui-He - A Triumvirate of AI-Driven Theoretical Discovery (paper): https://arxiv.org/abs/2405.19973 - Edward Frenkel explains the Geometric Langlands Correspondence on TOE: https://www.youtube.com/watch?v=RX1tZv_Nv4Y - Stone Duality (Wiki): https://en.wikipedia.org/wiki/Stone_duality - Summer of Math Exposition: https://some.3b1b.co/ - Machine Learning meets Number Theory: The Data Science of Birch–Swinnerton-Dyer (paper): https://arxiv.org/pdf/1911.02008 - The L-functions and modular forms database: https://www.lmfdb.org/ - Epoch AI FrontierMath: https://epoch.ai/frontiermath/the-benchmark - Mathematical Beauty (article): https://www.quantamagazine.org/mathematical-beauty-truth-and-proof-in-the-age-of-ai-20250430/ SUPPORT: - Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join - Support me on Patreon: https://patreon.com/curtjaimungal - Support me on Crypto: https://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - Support me on PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 SOCIALS: - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs #science Learn more about your ad choices. Visit megaphone.fm/adchoices

My guest today is Dr. Aditya Nagrath, who holds a PhD in Mathematics and Computer Science. With over 30 years of industry experience as a software engineer, author, and entrepreneur, he's worked on everything from atomic clocks to Amazon's Kindle Fire. As founder of Elephant Head Math software and the Elephant Learning Math Academy, he's developed an online system that helps children learn about a year and a half of math in just 10 weeks when used 30 minutes per week.   In our conversation, Dr. Nagrath outlines three distinct steps to master new math concepts – define, recognize, and produce. He explains the crucial "language gap" in mathematics, and explores the difference between recognizing math symbols on paper versus truly understanding and applying mathematical concepts. Most importantly, we discuss math anxiety and what children need to overcome it.   Get full show notes, transcript, and more information here: https://planningplaytime.com/101

In this episode of The Research Files podcast, Teacher editor Jo Earp chats to Jenni Ingram, Professor of Mathematics at the University of Oxford, about the OECD's Unlocking High-Quality Teaching report. Alongside insights from 150 schools in 50 countries, it explores 20 practices that teachers draw on to achieve 5 key teaching goals. Host: Jo Earp Guest: Professor Jenni Ingram

In this episode of Room to Grow, Joanie and Curtis continue the season 5 series on the Mathematics Teaching Practices from NCTM's Principles to Actions, celebrating its 10th anniversary. This month's practice is “Establish Mathematics Goals to Focus Learning.” This is defined as follows:Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions. In today's conversation, our hosts unpack the key components of this principle. First, they discuss how learning goals, focused on important mathematical understandings, differ from procedural, process goals, which may include skills and procedures that are not directly connected to the underlying mathematical concepts. Next, the discussion turns to situating goals within a learning progression, which helps teachers stay focused on what is relevant to their grade level or course, and provides a venue for students to be active in their progress toward learning. Finally, effective mathematics goals guide instructional decisions, helping educators know which tangents to explore and which are distractions from the intended learning. We hope you enjoy the conversation, and that it extends your thinking on mathematics goals for learning. Additional referenced content includes:·       NCTM's Principles to Actions·       NCTM's Taking Action series for grades K-5, grades 6-8, and grades 9-12·       NCTM's myNCTM forums (membership required).·       How learning goals serve as a guide – NCTM Teaching Children Mathematics blog post·       Rachel Harrington's appearance on the Math Learning Center podcast/blog discussing mathematical goals 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. 

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In his new book, Blueprints, Marcus du Sautoy traces the connections between mathematics and art and the ways in which creatives use numbers to underpin their work – unconsciously or otherwise. From the earliest stone circles to the unique architecture of Zaha Hadid, du Sautoy shows us that there are blueprints everywhere and how logic and aesthetics are intrinsically intermingled. Sophie Pavelle is also interested in connections and her forthcoming book, To Have or To Hold, explores symbiotic relationships in nature. Focusing on eight key examples, Sophie Pavelle explains how these mutually beneficial connections are crucial for the survival of our natural world and how they play an integral role in regulating ecosystems and strengthening resilience. She asks if we are capable of restoring and nurturing our environment or will we continue to exploit the Earth's resources, till death do us part? The British Museum's new exhibition illuminates the captivating work of the nineteenth-century Japanese artist, Utagawa Hiroshige (from 1st May to 7th September 2025). He was fascinated by the natural world and many of his pictures take flora and fauna as their subject matter. Hiroshige was one of Japan's most talented, prolific and popular artists and his influence was not only felt in his home country, but spread globally – influencing artists such as Vincent Van Gogh and contemporary artists such as Julian Opie. The curator of the exhibition, Alfred Haft, shines a light on the oeuvre of Hiroshige, his techniques and enduring legacy.Producer: Natalia Fernandez

Monday marks what would have been Malcolm X’s 100th birthday. Akinyele Umoja, a professor in the department of Africana Studies at Georgia State University, talks more about the Muslim minister and civil and human rights leader’s life and legacy, from his early years when he was known as “Detroit Red” to his period within the Nation of Islam. Professor Umoja also discusses his own involvement in the Malcolm X Grassroots Movement. INSERT: We continue with WABE’s “Server South” series. Residents in Fayetteville brace for rapid data center development, basically in their backyards, we air WABE Southside reporter DorMiya Vance’s latest report. Plus, for “Closer Look’s” Class of 2025 graduation series, we hear from Winter Jones. The standout graduate is part of Spelman College’s largest-ever graduating class, consisting of 694 students. While earning her degree, Jones became an astronaut scholar and worked with NASA on reducing emissions from supersonic jets. Now, Jones talks with Rose about her academic journey and her dreams of becoming an aerospace engineer.See omnystudio.com/listener for privacy information.

This episode of the Bitcoin Infinity Academy covers Sovereignty Through Mathematics Chapter 9: Money as an Amplifier In this episode, we explore the idea of money as a linguistic tool for expressing value and its role as an amplifier of personality. The discussion covers the flawed nature of fiat money, the societal impacts of sound money, the parallels between Bitcoin and gold, and much more!  Read the chapter on Nostr: https://dev.primal.net/infinity/sovereignty-through-mathematics-chapter-9:-money-as-an-amplifier Join the academy at our Geyser page: https://geyser.fund/project/infinity You can also support us by sending some sats to our Alby Hub at bitcoininfinity@getalby.com  The Bitcoin Infinity Academy is an educational project built around Knut Svanholm's books about Bitcoin and Austrian Economics. Each week, a whole chapter from one of the books is released for free on Highlighter, accompanied by a video in which Knut and Luke de Wolf discuss that chapter's ideas. You can join the discussions by signing up for one of the courses on our Geyser page! Connect with Us: https://www.bitcoininfinityshow.com/ https://bitcoininfinitystore.com https://primal.net/infinity https://primal.net/knut https://primal.net/luke https://twitter.com/BtcInfinityShow https://twitter.com/knutsvanholm https://twitter.com/lukedewolf

Can you hide in plain sight? Katherine Perry, assistant professor of mathematics at Soka University of America, explores if mathematics can. Katherine Perry is a mathematician specializing in graph theory, design theory, and combinatorics. She is especially interested in breaking apart graphs into smaller subgraphs with special properties. She has a BA in mathematics from […]

Tweetable quote from Fr. Seán“Life is a dream that the ego is having, the ego is a dream that the soul is having, and the soul is a dream that spirit is having.”SummaryJoin us for a profound conversation as we explore the depths of spirituality, faith, and the teachings of Christ with Fr. Seán ÓLaoire. He introduces the concept of Christ consciousness as a recognition of the inner divinity present in all beings. The dialogue explores the importance of small, supportive communities in spiritual growth, the significance of understanding sacred texts through a mystical lens, and the transformative power of personal experiences in healing and self-discovery.About our guest:Fr. Seán ÓLaoire, PhD, born in Cork, Ireland, holds a BSc in Mathematics and a PhD in Transpersonal Psychology. Ordained as a Catholic priest in 1972, he spent 14 years serving in East Africa and is fluent in six languages. He is a licensed Clinical Psychologist, author, and researcher focused on the effects of prayer. Fr. Seán is Co-Founder and Spiritual Director of Companions on the Journey, a non-hierarchical spiritual community that honors personal experience, interfaith wisdom, and the divine in all.

Episode: 1375 Leibniz, Newton, and the great calculus dispute.  Today, we throw Leibniz's cat into the super collider.

Stephen Wolfram is a physicists, mathematician, and programmer who believes he has discovered the computational rules that organize the universe at the finest grain. These rules are not physical rules like the equations of state or Maxwell's equations. According to Wolfram, these are rules that govern how the universe evolves and operates at a level at least one step down below the reality that we inhabit. His computational principles are inspired by the results observed in cellular automata systems, which show that it's possible to take a very simple system, with very simple rules, and end up at complex patterns that often look organic and always look far more intricate than the black and white squares that the game started with. We sit down with him for a conversation about the platonic endeavor that he has undertaken, where to draw the line between lived experience and the computational universe, the limits of physics, and the value of purpose and the source of consciousness. MAKE HISTORY WITH US THIS SUMMER:https://demystifysci.com/demysticon-2025PATREON https://www.patreon.com/c/demystifysciPARADIGM DRIFThttps://demystifysci.com/paradigm-drift-show00:00 Go!00:02:07 Entropy and Computational Irreducibility00:09:45 Understanding Observers in Physics00:15:12 The Concept of Time as Computation00:23:00 Neural Networks and Determinism00:30:03 Understanding Space and Its Nature00:39:24 Exploring the Nature of Emergence and Reality00:41:44 Perception and Computational Limitations of Human Minds00:46:18 The Complexity of Existence and Consciousness00:51:58 The Universe's Computation versus Human Understanding00:55:42 Conceptualizing Reality Beyond Physical Actors01:01:11 Computational Irreducibility in Biological Systems01:09:49 The Nature of Experience in Humans and Machines01:14:25 Internal Experiences and the Connection to Purpose01:18:07 Exploration of Purpose in Life and AI01:26:00 The Nature of Human Existence and Purpose01:35:19 Searching for Extraterrestrial Intelligence and Understanding Reality01:41:02 Communication Across Species02:01:13 Emergence of Simple Rules in Physics02:14:47 Observers and the Universe02:19:14 The Role of Mass and Experience02:24:02 Self-Reproduction and Evolution02:30:50 Complexity and Natural Selection02:37:07 Foundations of Medicine02:40:45 Application of Physics Concepts in Other Fields02:49:44 Limits and Possibilities of Travel Through Space02:53:11 Future of Human Civilization and Technology02:55:05 Science and Pre-Existing Questions about the Universe02:58:05 The Intersection of Mathematics and Physical Reality#physics, #computationalphysics, #consciousness, #freewill, #determinism, #spaceexploration, #evolution, #purpose, #futureofhumanity, #complexsystems , #machinelearning, #philosophypodcast , #sciencepodcast, #longformpodcast ABOUS US: Anastasia completed her PhD studying bioelectricity at Columbia University. When not talking to brilliant people or making movies, she spends her time painting, reading, and guiding backcountry excursions. Shilo also did his PhD at Columbia studying the elastic properties of molecular water. When he's not in the film studio, he's exploring sound in music. They are both freelance professors at various universities. PATREON: get episodes early + join our weekly Patron Chat https://bit.ly/3lcAasBMERCH: Rock some DemystifySci gear : https://demystifysci.myspreadshop.com/allAMAZON: Do your shopping through this link: https://amzn.to/3YyoT98DONATE: https://bit.ly/3wkPqaDSUBSTACK: https://substack.com/@UCqV4_7i9h1_V7hY48eZZSLw@demystifysciBLOG: http://DemystifySci.com/blog RSS: https://anchor.fm/s/2be66934/podcast/rssMAILING LIST: https://bit.ly/3v3kz2S SOCIAL: - Discord: https://discord.gg/MJzKT8CQub- Facebook: https://www.facebook.com/groups/DemystifySci- Instagram: https://www.instagram.com/DemystifySci/- Twitter: https://twitter.com/DemystifySciMUSIC: -Shilo Delay: https://g.co/kgs/oty671

On this episode of ID the Future from the archive, Andrew McDiarmid talks with science historian Michael Keas about pioneering mathematical astronomer Johannes Kepler, based on Keas's book Unbelievable: 7 Myths About the History and Future of Science and Religion. Kepler studied theology before turning to math and science, and it was his belief in God that guided his extraordinary discoveries. Kepler is one of several great scientists of early modern science whose convictions about God's nature inspired their groundbreaking investigations. Source

From the earliest stone circles to Mozart's obsession with numbers to the radically modern architecture of Zaha Hadid, maths and creativity are interwoven across time and space. Whether we are searching for meaning in an abstract painting or finding patterns in poetry, there are blueprints everywhere: symmetry, prime numbers, the golden ratio and more. In May 2025 we were joined by award-winning mathematician and Oxford professor Marcus du Sautoy as he looked to the arts to uncover the key mathematical structures that underpin both nature and human creativity. Drawing on his new book, Blueprints, du Sautoy explored how we make art, why a creative mindset is vital for discovering new mathematics, and how a fundamental connection to the natural world intrinsically links these two subjects. ----- If you'd like to become a Member and get access to all our full ad free conversations, plus all of our Members-only content, just visit intelligencesquared.com/membership to find out more. For £4.99 per month you'll also receive: - Full-length and ad-free Intelligence Squared episodes, wherever you get your podcasts - Bonus Intelligence Squared podcasts, curated feeds and members exclusive series - 15% discount on livestreams and in-person tickets for all Intelligence Squared events  ...  Or Subscribe on Apple for £4.99: - Full-length and ad-free Intelligence Squared podcasts - Bonus Intelligence Squared podcasts, curated feeds and members exclusive series … Already a subscriber? Thank you for supporting our mission to foster honest debate and compelling conversations! Visit intelligencesquared.com to explore all your benefits including ad-free podcasts, exclusive bonus content and early access. … Subscribe to our newsletter here to hear about our latest events, discounts and much more. https://www.intelligencesquared.com/newsletter-signup/ Learn more about your ad choices. Visit podcastchoices.com/adchoices Learn more about your ad choices. Visit podcastchoices.com/adchoices

Dr. John Mighton is an award-winning mathematician, playwright, and best-selling author internationally recognized for his ground-breaking work building children's confidence, skills, and success in math. He founded the Canadian charity JUMP Math (Junior Undiscovered Math Prodigies) in 2002 with an equity-driven mission to empower every child to achieve their potential through accessible math education. JUMP Math's K-8 resources currently support thousands of educators and students in North America and other countries to teach, learn, and love math. Dr. Mighton holds a master's degree in philosophy from McMaster University and a PhD in Mathematics from the University of Toronto, where he frequently teaches at the Ontario Institute for Studies in Education. A recipient of the Order of Canada, Dr. Mighton has published three books on math education, given hundreds of talks on the subject, including a TEDx Talk and keynote at the Aspen Brain Forum, and has received many awards and honorary doctorates in recognition of his work. His latest book, All Things Being Equal: Why Math is the Key to a Better World, offers a compelling argument for why accessible math education can and must be available to everyone. In a twist of fate in his early career, Dr. Mighton played Matt Damon's math tutor in the 1997 movie, Good Will Hunting ---- Stay Connected with #CanadasEntrepreneur! Join our growing community of entrepreneurs across Canada! Don't miss out on inspiring interviews, expert insights, and the latest business trends from the people shaping the future of our economy.

From the earliest stone circles to Mozart's obsession with numbers to the radically modern architecture of Zaha Hadid, maths and creativity are interwoven across time and space. Whether we are searching for meaning in an abstract painting or finding patterns in poetry, there are blueprints everywhere: symmetry, prime numbers, the golden ratio and more. In May 2025 we were joined by award-winning mathematician and Oxford professor Marcus du Sautoy as he looked to the arts to uncover the key mathematical structures that underpin both nature and human creativity. Drawing on his new book, Blueprints, du Sautoy explored how we make art, why a creative mindset is vital for discovering new mathematics, and how a fundamental connection to the natural world intrinsically links these two subjects. ------ This is the first instalment of a two-part episode. If you'd like to become a Member and get access to all our full ad free conversations, plus all of our Members-only content, just visit intelligencesquared.com/membership to find out more. For £4.99 per month you'll also receive: - Full-length and ad-free Intelligence Squared episodes, wherever you get your podcasts - Bonus Intelligence Squared podcasts, curated feeds and members exclusive series - 15% discount on livestreams and in-person tickets for all Intelligence Squared events  ...  Or Subscribe on Apple for £4.99: - Full-length and ad-free Intelligence Squared podcasts - Bonus Intelligence Squared podcasts, curated feeds and members exclusive series … Already a subscriber? Thank you for supporting our mission to foster honest debate and compelling conversations! Visit intelligencesquared.com to explore all your benefits including ad-free podcasts, exclusive bonus content and early access. … Subscribe to our newsletter here to hear about our latest events, discounts and much more. https://www.intelligencesquared.com/newsletter-signup/ Learn more about your ad choices. Visit podcastchoices.com/adchoices Learn more about your ad choices. Visit podcastchoices.com/adchoices

From Buffalo Bob to the NSA, we cover it all with magician and mathematician S. Brent Morris … and then jump into the next chapter of “The Linking Rings.” Brent Morris Interview starts at 00:05:44"I Love That" starts at 00:55:57Chapter Nine of "The Linking Rings" starts at 01:03:52 LINKSThe Eli Marks Mystery Series: http://www.elimarksmysteries.com/Get yourself a Free Eli Marks Short Story: https://dl.bookfunnel.com/jj1r1yaavjListen to an Eli Marks Audio Short Story: https://BookHip.com/LZBPPMDEmail John at jgaspard (at) earthlink (dot) netThe Tour Guy: https://thetourguy.com/Five Hours of The Shipping News: https://youtu.be/CxHa5KaMBcMCheck out the Occasional Film Podcast: https://www.fastcheapfilm.com/the-podcast

Is AI a big scam? In their co-authored new book, The AI Con, Emily Bender and Alex Hanna take aim at what they call big tech “hype”. They argue that large language models from OpenAI or Anthropic are merely what Bender dubs "stochastic parrots" that produce text without the human understanding nor the revolutionary technology that these companies claim. Both Bender, a professor of linguistics, and Hanna, a former AI researcher at Google, challenge the notion that AI will replace human workers, suggesting instead that these algorithms produce "mid" or "janky" content lacking human insight. They accuse tech companies of hyping fear of missing out (FOMO) to drive adoption. Instead of centralized AI controlled by corporations, they advocate for community-controlled technology that empowers users rather than exploiting them. Five Takeaways (with a little help from Claude)* Large language models are "stochastic parrots" that produce text based on probability distributions from training data without actual understanding or communicative intent.* The AI "revolution" is primarily driven by marketing and hype rather than groundbreaking technological innovations, creating fear of missing out (FOMO) to drive adoption.* AI companies are positioning their products as "general purpose technologies" like electricity, but LLMs lack the reliability and functionality to justify this comparison.* Corporate AI is designed to replace human labor and centralize power, which the authors see as an inherently political project with concerning implications.* Bender and Hanna advocate for community-controlled technology development where people have agency over the tools they use, citing examples like Teheku Media's language technology for Maori communities.Dr. Emily M. Bender is a Professor of Linguistics at the University of Washington where she is also the Faculty Director of the Computational Linguistics Master of Science program and affiliate faculty in the School of Computer Science and Engineering and the Information School. In 2023, she was included in the inaugural Time 100 list of the most influential people in AI. She is frequently consulted by policymakers, from municipal officials to the federal government to the United Nations, for insight into into how to understand so-called AI technologies.Dr. Alex Hanna is Director of Research at the Distributed AI Research Institute (DAIR). A sociologist by training, her work centers on the data used in new computational technologies, and the ways in which these data exacerbate racial, gender, and class inequality. She also works in the area of social movements, focusing on the dynamics of anti-racist campus protest in the US and Canada. She holds a BS in Computer Science and Mathematics and a BA in Sociology from Purdue University, and an MS and a PhD in Sociology from the University of Wisconsin-Madison. Dr. Hanna is the co-author of The AI Con (Harper, 2025), a book about AI and the hype around it. With Emily M. Bender, she also runs the Mystery AI Hype Theater 3000 series, playfully and wickedly tearing apart AI hype for a live audience online on Twitch and her podcast. She has published widely in top-tier venues across the social sciences, including the journals Mobilization, American Behavioral Scientist, and Big Data & Society, and top-tier computer science conferences such as CSCW, FAccT, and NeurIPS. Dr. Hanna serves as a Senior Fellow at the Center for Applied Transgender Studies and sits on the advisory board for the Human Rights Data Analysis Group. She is also recipient of the Wisconsin Alumni Association's Forward Award, has been included on FastCompany's Queer 50 (2021, 2024) List and Business Insider's AI Power List, and has been featured in the Cal Academy of Sciences New Science exhibit, which highlights queer and trans scientists of color.Named as one of the "100 most connected men" by GQ magazine, Andrew Keen is amongst the world's best known broadcasters and commentators. In addition to presenting the daily KEEN ON show, he is the host of the long-running How To Fix Democracy interview series. He is also the author of four prescient books about digital technology: CULT OF THE AMATEUR, DIGITAL VERTIGO, THE INTERNET IS NOT THE ANSWER and HOW TO FIX THE FUTURE. Andrew lives in San Francisco, is married to Cassandra Knight, Google's VP of Litigation & Discovery, and has two grown children.Keen On America is a reader-supported publication. To receive new posts and support my work, consider becoming a free or paid subscriber. This is a public episode. If you'd like to discuss this with other subscribers or get access to bonus episodes, visit keenon.substack.com/subscribe

This episode of the Bitcoin Infinity Academy covers Sovereignty Through Mathematics Chapter 8: Changing the Rules In this episode, we explore the intricacies of altering the Bitcoin protocol,t he concepts of hard forks and soft forks, and more. We also touch on historical events such as the block size wars, the difference between Bitcoin and crypto, and the idea of Bitcoin as absolute digital scarcity. Read the chapter on Nostr: https://primal.net/infinity/sovereignty-through-mathematics-chapter-8:-changing-the-rules Join the academy at our Geyser page: https://geyser.fund/project/infinity You can also support us by sending some sats to our Alby Hub at bitcoininfinity@getalby.com The Bitcoin Infinity Academy is an educational project built around Knut Svanholm's books about Bitcoin and Austrian Economics. Each week, a whole chapter from one of the books is released for free on Highlighter, accompanied by a video in which Knut and Luke de Wolf discuss that chapter's ideas. You can join the discussions by signing up for one of the courses on our Geyser page! Connect with Us: https://www.bitcoininfinityshow.com/ https://bitcoininfinitystore.com https://primal.net/infinity https://primal.net/knut https://primal.net/luke https://twitter.com/BtcInfinityShow https://twitter.com/knutsvanholm https://twitter.com/lukedewolf

Episode109-Marta Garcia, "Redefining Mathematics For Belonging"

Stephen Wolfram answers questions from his viewers about the future of science and technology as part of an unscripted livestream series, also available on YouTube here: https://wolfr.am/youtube-sw-qaTopics discussed: Fusion energy and nuclear fuel design - AI reasoning, learning and scientific roles - Mathematics, computation and physical reality - Jobs and fields at risk from AI - Philosophy of knowledge and future roles

William Zahner, Understanding the Role of Language in Math Classrooms ROUNDING UP: SEASON 3 | EPISODE 17 How can educators understand the relationship between language and the mathematical concepts and skills students engage with in their classrooms? And how might educators think about the mathematical demands and the language demands of tasks when planning their instruction?  In this episode, we discuss these questions with Bill Zahner, director of the Center for Research in Mathematics and Science Education at San Diego State University. BIOGRAPHY Bill Zahner is a professor in the mathematics department at San Diego State University and the director of the Center for Research in Mathematics and Science Education. Zahner's research is focused on improving mathematics learning for all students, especially multilingual students who are classified as English Learners and students from historically marginalized communities that are underrepresented in STEM fields. RESOURCES Teaching Math to Multilingual Learners, Grades K–8 by Kathryn B. Chval, Erin Smith, Lina Trigos-Carrillo, and Rachel J. Pinnow National Council of Teachers of Mathematics Mathematics Teacher: Learning and Teaching PK– 12 English Learners Success Forum SDSU-ELSF Video Cases for Professional Development The Math Learning Center materials Bridges in Mathematics curriculum Bridges in Mathematics Teachers Guides [BES login required] TRANSCRIPT Mike Wallus: How can educators understand the way that language interacts with the mathematical concepts and skills their students are learning? And how can educators focus on the mathematics of a task without losing sight of its language demands as their planning for instruction? We'll examine these topics with our guest, Bill Zahner, director of the Center for Research in Mathematics and Science Education at San Diego State University.  Welcome to the podcast, Bill. Thank you for joining us today. Bill Zahner: Oh, thanks. I'm glad to be here. Mike: So, I'd like to start by asking you to address a few ideas that often surface in conversations around multilingual learners and mathematics. The first is the notion that math is universal, and it's detached from language. What, if anything, is wrong with this idea and what impact might an idea like that have on the ways that we try to support multilingual learners? Bill: Yeah, thanks for that. That's a great question because I think we have a common-sense and strongly held idea that math is math no matter where you are and who you are. And of course, the example that's always given is something like 2 plus 2 equals 4, no matter who you are or where you are. And that is true, I guess [in] the sense that 2 plus 2 is 4, unless you're in base 3 or something. But that is not necessarily what mathematics in its fullness is. And when we think about what mathematics broadly is, mathematics is a way of thinking and a way of reasoning and a way of using various tools to make sense of the world or to engage with those tools [in] their own right. And oftentimes, that is deeply embedded with language.  Probably the most straightforward example is anytime I ask someone to justify or explain what they're thinking in mathematics. I'm immediately bringing in language into that case. And we all know the old funny examples where a kid is asked to show their thinking and they draw a diagram of themselves with a thought bubble on a math problem. And that's a really good case where I think a teacher can say, “OK, clearly that was not what I had in mind when I said, ‘Show your thinking.'”  And instead, the demand or the request was for a student to show their reasoning or their thought process, typically in words or in a combination of words and pictures and equations. And so, there's where I see this idea that math is detached from language is something of a myth; that there's actually a lot of [language in] mathematics. And the interesting part of mathematics is often deeply entwined with language. So, that's my first response and thought about that.  And if you look at our Common Core State Standards for Mathematics, especially those standards for mathematical practice, you see all sorts of connections to communication and to language interspersed throughout those standards. So, “create viable arguments,” that's a language practice. And even “attend to precision,” which most of us tend to think of as, “round appropriately.” But when you actually read the standard itself, it's really about mathematical communication and definitions and using those definitions with precision. So again, that's an example, bringing it right back into the school mathematics domain where language and mathematics are somewhat inseparable from my perspective here. Mike: That's really helpful. So, the second idea that I often hear is, “The best way to support multilingual learners is by focusing on facts or procedures,” and that language comes later, for lack of a better way of saying it. And it seems like this is connected to that first notion, but I wanted to ask the question again: What, if anything, is wrong with this idea that a focus on facts or procedures with language coming after the fact? What impact do you suspect that that would have on the way that we support multilingual learners? Bill: So, that's a great question, too, because there's a grain of truth, right? Both of these questions have simultaneously a grain of truth and simultaneously a fundamental problem in them. So, the grain of truth—and an experience that I've heard from many folks who learned mathematics in a second language—was that they felt more competent in mathematics than they did in say, a literature class, where the only activity was engaging with texts or engaging with words because there was a connection to the numbers and to symbols that were familiar. So, on one level, I think that this idea of focusing on facts or procedures comes out of this observation that sometimes an emergent multilingual student feels most comfortable in that context, in that setting.  But then the second part of the answer goes back to this first idea that really what we're trying to teach students in school mathematics now is not simply, or only, how to apply procedures to really big numbers or to know your times tables fast. I think we have a much more ambitious goal when it comes to teaching and learning mathematics. That includes explaining, justifying, modeling, using mathematics to analyze the world and so on. And so, those practices are deeply tied with language and deeply tied with using communication. And so, if we want to develop those, well, the best way to do that is to develop them, to think about, “What are the scaffolds? What are the supports that we need to integrate into our lessons or into our designs to make that possible?”  And so, that might be the takeaway there, is that if you simply look at mathematics as calculations, then this could be true. But I think our vision of mathematics is much broader than that, and that's where I see this potential. Mike: That's really clarifying. I think the way that you unpack that is if you view mathematics as simply a set of procedures or calculations, maybe? But I would agree with you. What we want for students is actually so much more than that.  One of the things that I heard you say when we were preparing for this interview is that at the elementary level, learning mathematics is a deeply social endeavor. Tell us a little bit about what you mean by that, Bill. Bill: Sure. So, mathematics itself, maybe as a premise, is a social activity. It's created by humans as a way of engaging with the world and a way of reasoning. So, the learning of mathematics is also social in the sense that we're giving students an introduction to this way of engaging in the world. Using numbers and quantities and shapes in order to make sense of our environment.  And when I think about learning mathematics, I think that we are not simply downloading knowledge and sticking it into our heads. And in the modern day where artificial intelligence and computers can do almost every calculation that we can imagine—although your AI may do it incorrectly, just as a fair warning [laughs]—but in the modern day, the actual answer is not what we're so focused on. It's actually the process and the reasoning and the modeling and justification of those choices. And so, when I think about learning mathematics as learning to use these language tools, learning to use these ways of communication, how do we learn to communicate? We learn to communicate by engaging with other people, by engaging with the ideas and the minds and the feelings and so on of the folks around us, whether it's the teacher and the student, the student and the student, the whole class and the teacher. That's where I really see the power. And most of us who have learned, I think can attest to the fact that even when we're engaging with a text, really fundamentally we're engaging with something that was created by somebody else. So, fundamentally, even when you're sitting by yourself doing a math word problem or doing calculations, someone has given that to you and you think that that's important enough to do, right?  So, from that stance, I see all of teaching and learning mathematics is social. And maybe one of our goals in mathematics classrooms, beyond memorizing the times tables, is learning to communicate with other people, learning to be participants in this activity with other folks. Mike: One of the things that strikes me about what you were saying, Bill, is there's this kind of virtuous cycle, right? That by engaging with language and having the social aspect of it, you're actually also deepening the opportunity for students to make sense of the math. You're building the scaffolds that help kids communicate their ideas as opposed to removing or stripping out the language. That's the context in some ways that helps them filter and make sense. You could either be in a vicious cycle, which comes from removing the language, or a virtuous cycle. And it seems a little counterintuitive because I think people perceive language as the thing that is holding kids back as opposed to the thing that might actually help them move forward and make sense. Bill: Yeah. And actually that's one of the really interesting pieces that we've looked at in my research and the broader research is this question of, “What makes mathematics linguistically complex?” is a complicated question. And so sometimes we think of things like looking at the word count as a way to say, “If there are fewer words, it's less complex, and if there are more words, it's more complex.” But that's not totally true. And similarly, “If there's no context, it's easier or more accessible, and if there is a context, then it's less accessible.”  And I don't see these as binary choices. I see these as happening on a somewhat complicated terrain where we want to think about, “How do these words or these contexts add to student understanding or potentially impede [it]?” And that's where I think this social aspect of learning mathematics—as you described, it could be a virtuous cycle so that we can use language in order to engage in the process of learning language. Or, the vicious cycle is, you withhold all language and then get frustrated when students can't apply their mathematics. That's maybe the most stereotypical answer: “My kids can do this, but as soon as they get a word problem, they can't do it.” And it's like, “Well, did you give them opportunities to learn how to do this? [laughs] Or is this the first time?” Because that would explain a lot. Mike: Well, it's an interesting question, too, because I think what sits behind that in some ways is the idea that you're kind of going to reach a point, or students might reach a point, where they're “ready” for word problems.  Bill: Right. Mike: And I think what we're really saying is it's actually through engaging with word problems that you build your proficiency, your skillset that actually allows you to become a stronger mathematician. Bill: Mm-hmm. Right. Exactly. And it's a daily practice, right? It's not something that you just hold off to the end of the unit, and then you have the word problems, but it's part of the process of learning. And thinking about how you integrate and support that. That's the key question that I really wrestle with. Not trivial, but I think that's the key and the most important part of this. Mike: Well, I think that's actually a really good segue because I wanted to shift and talk about some of the concrete or productive ways that educators can support multilingual learners. And in preparing for this conversation, one of the things that I've heard you stress is this notion of a consistent context. So, can you just talk a little bit more about what you mean by that and how educators can use that when they're looking at their lessons or when they're writing lessons or looking at the curriculum that they're using? Bill: Absolutely. So, in our past work, we engaged in some cycles of design research with teachers looking at their mathematics curriculum and opportunities to engage multilingual learners in communication and reasoning in the classroom. And one of the surprising things that we found—just by looking at a couple of standard textbooks—was a surprising number of contexts were introduced that are all related to the same concept. So, the concept would be something like rate of change or ratio, and then the contexts, there would be a half dozen of them in the same section of the book. Now, this was, I should say, at a secondary level, so not quite where most of the Bridges work is happening. But I think it's an interesting lesson for us that we took away from this. Actually, at the elementary level, Kathryn Chval has made the same observation.  What we realized was that contexts are not good or bad by themselves. In fact, they can be highly supportive of student reasoning or they can get in the way. And it's how they are used and introduced. And so, the other way we thought about this was: When you introduce a context, you want to make sure that that context is one that you give sufficient time for the students to understand and to engage with; that is relatable, that everyone has access to it; not something that's just completely unrelated to students' experiences. And then you can really leverage that relatable, understandable context for multiple problems and iterations and opportunities to go deeper and deeper.  To give a concrete example of that, when we were looking at this ratio and rate of change, we went all the way back to one of the fundamental contexts that's been studied for a long time, which is motion and speed and distance and time. And that seemed like a really important topic because we know that that starts all the way back in elementary school and continues through college-level physics and beyond. So, it was a rich context. It was also something that was accessible in the sense that we could do things like act out story problems or reenact a race that's described in a story problem. And so, the students themselves had access to the context in a deep way.  And then, last, that context was one that we could come back to again and again, so we could do variations [of] that context on that story. And I think there's lots of examples of materials out there that start off with a core context and build it out. I'm thinking of some of the Bridges materials, even on the counting and the multiplication. I think there's stories of the insects and their legs and wings and counting and multiplying. And that's a really nice example of—it's accessible, you can go find insects almost anywhere you are. Kids like it. [Laughs] They enjoy thinking about insects and other icky, creepy-crawly things. And then you can take that and run with it in lots of different ways, right? Counting, multiplication, division ratio, and so on. Mike: This last bit of our conversation has me thinking about what it might look like to plan a lesson for a class or a group of multilingual learners. And I know that it's important that I think about mathematical demands as well as the language demands of a given task. Can you unpack why it's important to set math and language development learning goals for a task, or a set of tasks, and what are the opportunities that come along with that, if I'm thinking about both of those things during my planning? Bill: Yeah, that's a great question. And I want to mark the shift, right? We've gone from thinking about the demands to thinking about the goals, and where we're going to go next.  And so, when I think about integrating mathematical goals—mathematical learning goals and language learning goals—I often go back to these ideas that we call the practices, or these standards that are about how you engage in mathematics. And then I think about linking those back to the content itself. And so, there's kind of a two-piece element to that. And so, when we're setting our goals and lesson planning, at least here in the great state of California, sometimes we'll have these templates that have, “What standard are you addressing?,” [Laughs] “What language standard are you addressing?,” “What ELD standard are you addressing?,” “What SEL standard are you addressing?” And I've seen sometimes teachers approach that as a checkbox, right? Tick, tick, tick, tick, tick. But I see that as a missed opportunity—if you just look at this like you're plugging things in—because as we started with talking about how learning mathematics is deeply social and integrated with language, that we can integrate the mathematical goals and the language goals in a lesson. And I think really good materials should be suggesting that to the teacher. You shouldn't be doing this yourself every day from scratch. But I think really high-quality materials will say, “Here's the mathematical goal, and here's an associated language goal,” whether it's productive or receptive functions of language. “And here's how the language goal connects the mathematical goal.”  Now, just to get really concrete, if we're talking about an example of reasoning with ratios—so I was going back to that—then it might be generalized, the relationship between distance and time. And that the ratio of distance and time gives you this quantity called speed, and that different combinations of distance and time can lead to the same speed. And so, explain and justify and show using words, pictures, diagrams. So, that would be a language goal, but it's also very much a mathematical goal.  And I guess I see the mathematical content, the practices, and the language really braided together in these goals. And that I think is the ideal, and at least from our work, has been most powerful and productive for students. Mike: This is off script, but I'm going to ask it, and you can pass if you want to.  Bill: Mm-hmm. Mike: I wonder if you could just share a little bit about what the impact of those [kinds] of practices that you described [have been]—have you seen what that impact looks like? Either for an educator who has made the step and is doing that integration or for students who are in a classroom where an educator is purposely thinking about that level of integration? Bill: Yeah, I can talk a little bit about that. In our research, we have tried to measure the effects of some of these efforts. It is a difficult thing to measure because it's not just a simple true-false test question type of thing that you can give a multiple-choice test for.  But one of the ways that we've looked for the impact [of] these types of intentional designs is by looking at patterns of student participation in classroom discussions and seeing who is accessing the floor of the discussion and how. And then looking at other results, like giving an assessment, but deeper than looking at the outcome, the binary correct versus incorrect. Also looking at the quality of the explanation that's provided. So, how [do] you justify an answer? Does the student provide a deeper or a more mathematically complete explanation?  That is an area where I think more investigation is needed, and it's also very hard to vary systematically. So, from a research perspective—you may not want to put this into the final version [laughs]—but from a research perspective, it's very hard to fix and isolate these things because they are integrated. Mike: Yeah. Yeah. Bill: Because language and mathematics are so deeply integrated that trying to fix everything and do this—“What caused this water to taste like water? Was it the hydrogen or the oxygen?”—well, [laughs] you can't really pull those apart, right? The water molecule is hydrogen and oxygen together. Mike: I think that's a lovely analogy for what we were talking about with mathematical goals and language goals. That, I think, is really a helpful way to think about the extent to which they're intertwined with one another. Bill: Yeah, I need to give full credit to Vygotsky, I think, who said that. Mike: You're— Bill: Something. Might be Vygotsky. I'll need to check my notes. Mike: I think you're in good company if you're quoting Vygotsky.  Before we close, I'd love to just ask you a bit about resources. I say this often on the podcast. We have 20 to 25 minutes to dig deeply into an idea, and I know people who are listening often think about, “Where do I go from here?” Are there any particular resources that you would suggest for someone who wanted to continue learning about what it is to support multilingual learners in a math classroom? Bill: Sure. Happy to share that.  So, I think on the individual and collective level—so, say, a group of teachers—there's a beautiful book by Kathryn Chval and her colleagues [Teaching Math to Multilingual Learners, Grades K–8] about supporting multilingual learners and mathematics. And I really see that as a valuable resource. I've used that in reading groups with teachers and used that in book studies, and it's been very productive and powerful for us. Beyond that, of course, I think the NCTM [National Council of Teachers of Mathematics] provides a number of really useful resources. And there are articles, for example, in the [NCTM journal] Mathematics Teacher: Learning and Teaching PK– 12 that could make for a really wonderful study or opportunity to engage more deeply.  And then I would say on a broader perspective, I've worked with organizations like the English Learners Success Forum and others. We've done some case studies and little classroom studies that are accessible on my website [SDSU-ELSF Video Cases for Professional Development], so you can go to that. But there's also from that organization some really valuable insights, if you're looking at adopting new materials or evaluating things, that gives you a principled set of guidelines to follow. And I think that's really helpful for educators because we don't have to do this all on our own. This is not a “reinvent the wheel at every single site” kind of situation. And so, I always encourage people to look for those resources.  And of course, I will say that the MLC materials, the Bridges in Mathematics [curriculum], I think have been really beautifully designed with a lot of these principles right behind them. So, for example, if you look through the Teachers Guides on the Bridges in Mathematics [BES login required], those integrated math and language and practice goals are a part of the design. Mike: Well, I think that's a great place to stop. Thank you so much for joining us, Bill. This has been insightful, and it's really been a pleasure talking with you. Bill: Oh, well, thank you. I appreciate it. Mike: And that's a wrap for Season 3 of Rounding Up. I want to thank all of our guests and the MLC staff who make these podcasts possible, as well as all of our listeners for tuning in. Have a great summer, and we'll be back in September for Season 4.  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  

Show #2405 Show Notes: Luke 8: https://www.biblegateway.com/passage/?search=Luke%208&version=KJV ‘Manifest’: https://webstersdictionary1828.com/Dictionary/manifest LAN Events: https://thelibertyactionnetwork.com/calendar/ Mathematics of the Mound Builders: https://www.youtube.com/watch?v=NZDYuo2bGrM Parasites in Tumor: https://www.facebook.com/reel/919497673449737 Cancer-Fighting benefits of Ivermectin: https://choiceclips.whatfinger.com/2025/05/07/the-remarkable-cancer-fighting-benefits-of-ivermectin-ivermectin-can-actually-kill-cancer-stem-cells-which-are-often-resistant-to-chemotherapy/ New Cancer Treatment Protocol: https://www.thegatewaypundit.com/2024/10/new-cancer-treatment-protocol-featuring-horse-dewormer-ivermectin/ Government Admits it knew covid […]

Happy Teacher Appreciation week! This has been a whirlwind of a year and I address that briefly in the opening if you want to skip that, just to 3:00 minutes in.  In this episode, we sit down with Jaime Suarez, the 2025 Florida Teacher of the Year. A dedicated mathematics educator at Challenger K-8 School of Science and Mathematics in Hernando County, Jaime shares her journey from classroom teacher to state ambassador for education. As the Christa McAuliffe Ambassador for Education, Jaime discusses her mission to elevate the teaching profession and advocate for educators across Florida. Tune in to hear her insights on mentorship, leadership, and the transformative power of education. Note: For more information on Jaime Suarez's achievements and her role as Florida's Teacher of the Year, visit the Florida Department of Education's official announcement.

Learning to teach math teachers better with Dr. Gina Wilson, Knowles Teacher Initiative Program Officer of Teacher Development and Dr. Ayanna Perry, Director of Outreach and Dissemination, as we discuss supporting early career mathematics teachers and the professional development of teachers outside of higher education. Links from the episode Knowles Teacher Initiative (https://knowlesteachers.org/) Knowles Teaching Fellowship (https://knowlesteachers.org/teaching-fellowship) Knowles Academy (https://knowlesteachers.org/professional-learning) Knowles Annual Conference (https://knowlesteachers.org/annual-conference) Five to Thrive Series from Corwin (https://www.corwin.com/landing-pages/five-to-thrive-series?srsltid=AfmBOooIErSKqgBQnpGPBSfApHlKXHdCVHQTzCibmd8OdhLstekAxbi1) The Art of Coaching: Effective Strategies for School Transformation (https://www.google.com/books/edition/The_Art_of_Coaching/m_kZ7eO2q9UC?hl=en&gbpv=0) Mathematics Teacher Education Partnership (https://linktr.ee/mtep2.0) Special Guests: Ayanna Perry and Gina Wilson.

Dr. Theresa Bullard delves into the history of the split between physics and metaphysics, exploring its implications for our understanding of reality. She examines the laws of science that limit our perceptions and discusses her transformative shift from classical to quantum physics. She explains the mathematics of the universe, the 7 steps of the alchemical process, and how to embrace a quantum mindset. Try MUDWTR & Get Up to 43% off + a free frother:https://mudwtr.com/knowthyselfAndrés Book Recs: https://www.knowthyself.one/books___________0:00 Intro2:07 History of the Split between Physics & Metaphysics 7:32 Laws of Science that Limit Us10:54 Her Shift from Classical to Quantum Physics 17:00 The Implicate Order (New Science)27:00 Mathematics of the Universe31:41 (Mindset) Transcend Limitation, Embrace Quantum Possibility38:35 Embracing the Uncertainty of Life44:27 Ad: Mudwtr Save 43%46:05 How New Age Spirituality Mis-uses Quantum Terms56:53 The Science of Alchemy1:01:56 7 Steps of Alchemy (Personal Transformation) 1:17:28 Honoring Your Past While Moving Forward1:23:08 Our Inner Alchemical Process1:26:16 The Transformations that Shaped Her Life1:29:17 How Our DNA Evolves as we Awaken1:36:33 Science of Extra Sensory Perceptions1:46:36 Creating Coherence in Body, Mind & Soul1:51:29 Entrainment: Take Your Future Into Your Hands1:58:39 Practices to Becoming an Alchemist 2:05:12 Activate Your Divine Potential2:12:00 Conclusion ___________Episode Resources: https://theresabullard.comhttps://modernmysteryschoolint.com www.quantumlearningacademy.co https://www.instagram.com/andreduqum/https://www.instagram.com/knowthyself/https://www.youtube.com/@knowthyselfpodcasthttps://www.knowthyself.oneListen to the show:Spotify: https://spoti.fi/4bZMq9lApple: https://apple.co/4iATICX

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Many of us have plenty of experiences with math, especially when we were younger. Perhaps some of your memories of what math was like for you in school are unpleasant, to say the least. Yet there are many people who are passionate about mathematics, especially Christians who see mathematics as the God-given language by which we can better understand not only the physical world around us, but God Himself. Naturalism has no real answers for why mathematics is so useful and even beautiful and practical not only for doing science, but in our everyday lives. And how are beauty and mathematics linked? What do beauty and math tell us about God Himself? This week we wrap up our conversation with youth leader, math professor, friend of Watchman Fellowship and Christian apologist Paige Lehrmann. Paige will share with us her passion about mathematics, beauty, and how we can incorporate them in our defense for the hope that is in us (1 Peter 3:15). Paige Lehrmann is the Director of Student Ministries at St. Andrew's Community Church in Oklahoma City and a student at Dallas Theological Seminary. She earned her B.A. in Philosophy and Mathematics from Oklahoma Baptist University, where she completed an interdisciplinary thesis on the Trinity. Paige went on to pursue graduate studies in mathematics at the University of Oklahoma and has taught as an adjunct professor at Mid-America Christian University. She has presented at apologetics conferences on topics such as the Trinity, the divinity of Christ, and theistic arguments from beauty. Through her work, she hopes to help others think deeply about faith, truth, and the beauty of the Gospel.You may contact Paige via email at Paige.lehrmann@gmail.com. Free Resources from Watchman Fellowship Atheist New Testament scholar Dr. Bart D. Ehrman: www.watchman.org/Ehrman  Atheism: www.watchman.org/Atheism  Latter-day Saints: www.watchman.org/Mormonism Panpsychism: https://www.watchman.org/files/ProfilePanpsychism.pdf The New Age Movement: https://www.watchman.org/profiles/pdf/newageprofile.pdf Hinduism: https://www.watchman.org/staff/jwalker/ProfileHinduism.pdf Additional ResourcesFREE: We are also offering a subscription to our 4-page bimonthly Profiles here: www.watchman.org/FreePROFILE NOTEBOOK: Order the complete collection of Watchman Fellowship Profiles (around 700 pages -- from Astrology to Zen Buddhism) in either printed or PDF formats here: www.watchman.org/NotebookSUPPORT: Help us create more content like this. Make a tax-deductible donation here: www.watchman.org/GiveApologetics Profile is a ministry of Watchman Fellowship For more information, visit www.watchman.org © 2025 Watchman Fellowship, Inc.

Colton Carlson is a retired US Marine who lost his legs from injuries sustained during a tour of duty in Afghanistan. Originally from Colorado, home of The Rocky Mountains, Colton joins us from his home in Vermont, where he and his family settled after Colton earned a degree in Mathematics from Dartmouth. In this episode of Nature Revisited, Colton talks about his life before and after his assignment, his life-changing incident on duty, and how his love of nature helped him overcome immense challenges to reclaim his health, independence, and pursuit of outdoor activities and sports including his passion: mountain climbing. [Originally published nov 14, 2023. Ep 108] Listen to Nature Revisited on your favorite podcast apps or at https://noordenproductions.com Subscribe on Spotify: https://tinyurl.com/bdz4s9d7 Subscribe on Apple Podcasts: https://tinyurl.com/5n7yx28t Podlink: https://pod.link/1456657951 Support Nature Revisited https://noordenproductions.com/support Nature Revisited is produced by Stefan van Norden and Charles Geoghegan. We welcome your comments, questions and suggestions - contact us at https://noordenproductions.com/contact

Send us a textIn this episode of Petey Podcast, we celebrate a groundbreaking victory for the Elyria Robotics Team 44113T of middle school students who made history by earning the State Championship Title at a VEX Robotics tournament held at the Museum of the US Air Force in Dayton —the first time ever for any middle school in our district. Hear from the young champions themselves as they share what the win means to them, and meet some of their incredible teammates who also brought home top honors for excellence in sportsmanship.It's a great day to be a Pioneer! Thanks for listening. Find Elyria Schools on Facebook, Twitter, Instagram and YouTube!

It's commonly believed that the arts and the sciences have little in common with each other. The distinction that's most frequently made is that the arts are creative in nature whereas the sciences are logical. But this couldn't be further from the truth. In this episode, we catch up with mathematician and author Marcus du Sautoy to talk about his latest book Blueprints: How mathematics shapes creativity. He tells us how, fundamentally, mathematics is the study of patterns, structure and symmetry, how these patterns are found everywhere in music, visual art and architecture, and why we should be teaching students how to spot them in their everyday lives. Learn more about your ad choices. Visit podcastchoices.com/adchoices

In this episode of 10x Your Team, Camden and Otis McGregor are joined by Marc Fitzwater to explore the importance of values and grace in leadership. Marc shares his insights on how personal values shape leadership styles and the significance of allowing grace in professional relationships. The discussion delves into the challenges of aligning values within a team, the impact of diverse perspectives, and the role of open communication in fostering a collaborative environment. Whether you're a seasoned leader or just starting out, this episode offers valuable perspectives on building a cohesive and values-driven team.More About Marc:Marc Fitzwater, a retired Green Beret with 23 years in the U.S. Army (16 in Special Forces), served in high-stakes roles across Central and South America, Afghanistan, Iraq, and Eastern Europe. He held key leadership positions, including Team Sergeant of a modern Jedburgh Team and NCOIC of FIRES for the 10th Special Forces Group, overseeing JTAC training. Marc also worked at the strategic level with SOCNORTH, coordinating Special Operations and interagency efforts. Academically, he holds a Mathematics degree and a Master's in International Relations. Today, he runs I68 Consulting Group, offering defensive shooting training and community events like the Hounds & Hollow Points competition, which supports veterans through Victory Service Dogs. Marc's post-military mission focuses on empowering individuals and fostering veteran community engagement.Chapter Titles and Times:Introduction to Marc Fitzwater [00:00 - 05:00]Overview of Marc's background and expertiseIntroduction to the episode's themesThe Importance of Values in Leadership [05:01 - 15:00]Discussion on how personal values influence leadership stylesThe challenges of aligning values within a teamAllowing Grace in Professional Relationships [15:01 - 25:00]The significance of grace in fostering collaborationExamples of grace in action within teamsDiverse Perspectives and Open Communication [25:01 - 35:00]The impact of diverse perspectives on team dynamicsStrategies for encouraging open communicationBuilding a Cohesive Team [35:01 - 45:00]Tips for creating a values-driven team environmentMarc's insights on leadership and team cohesionClosing Thoughts and Takeaways [45:01 - End]Final reflections from Marc and the hostsKey takeaways for leaders looking to enhance their team dynamics#10xYourTeam #CamAndOtis #MarcFitzwater #LeadershipWithValues #GraceInLeadership #SpecialForcesLeadership #GreenBeretWisdom #TeamAlignment #ValuesDrivenLeadership #OpenCommunication #CollaborativeLeadership #VeteranLeadership #EmpowerYourTeam #DiversePerspectives #LeadershipChallenges #BuildingStrongTeams #I68Consulting #LeadershipJourney #MissionDrivenLeadership #VeteransEmpoweringCommunitiesMarc FitzwaterWebsite: https://www.i68consulting.com/Instagram: https://www.instagram.com/i68consultinggroupFacebook: https://www.facebook.com/I68consulting/LinkedIn: https://www.linkedin.com/in/marc-fitzwater-476686178/

Dharmendra Modha's TrueNorth chip added the word neuromorphic to the technorati lexicon back in 2014. In this episode of Brains and Machines, he talks to Sunny Bains of University College London about how that project led to his work on NorthPole and the axiomatic approach he took to design. 

This episode of the Bitcoin Infinity Academy covers Sovereignty Through Mathematics Chapter 7: Holding On In this episode, we explore the historic and financial implications of inflation, saving versus hodling, and the unprecedented scarcity of Bitcoin compared to traditional assets like gold and real estate. We also touch on the psychological aspects of delayed gratification, institutional adoption, and the potent potential for a global wealth transfer through Bitcoin.  Read the chapter on Nostr: https://primal.net/infinity/sovereignty-through%20mathematics%20chapter%207:%20holding%20on Join the academy at our Geyser page: https://geyser.fund/project/infinity You can also support us by sending some sats to our Alby Hub at bitcoininfinity@getalby.com The Bitcoin Infinity Academy is an educational project built around Knut Svanholm's books about Bitcoin and Austrian Economics. Each week, a whole chapter from one of the books is released for free on Highlighter, accompanied by a video in which Knut and Luke de Wolf discuss that chapter's ideas. You can join the discussions by signing up for one of the courses on our Geyser page! Connect with Us: https://www.bitcoininfinityshow.com/ https://bitcoininfinitystore.com https://primal.net/infinity https://primal.net/knut https://primal.net/luke https://twitter.com/BtcInfinityShow https://twitter.com/knutsvanholm https://twitter.com/lukedewolf

Send us a textOn this episode of Speaking Of…College of Charleston, we sit down with President Andrew T. Hsu to reflect on highlights of the year. From reaching an all time high of 32,000 applicants to establishing new academic programs like the BA in entrepreneurship, Hsu talks about his drive to keep moving, full speed ahead, to ensure the College's position as a leader of academic excellence.Some key achievements in the last year include the reorganization of STEM programs into two schools; the School of Natural and Environmental Sciences and the School of Engineering, Computing, and Mathematics. "Splitting stems into these two schools gives our university more precision, more flexibility and certainly more visibility across diverse scientific and technological domains, while still allowing for interdisciplinary collaboration," says Hsu.President Hsu emphasizes the importance of liberal arts education for developing durable skills in graduates to make them competitive in the work force. "When I talk with industry leaders, they are looking for graduates, not just with just technical skills, which can be learned on the job, but they want people with durable skills such as communication, creativity, teamwork, problem solving, emotional intelligence and a global mindset. These skills will help our students stay relevant far into the future. And and those are the types of graduates we're producing across disciplines."He reflects on proud moments from the year, including the college's national visibility and events such as the College of Charleston Orchestra's performance at one of the most prestigious stages in the world — Carnegie Hall.“Each of these moments showcase how amazing our university is. Truly, extraordinary events happen here at the College of Charleston every single day,” says Hsu. We are not going to argue.Resources From This episode:College of Charleston Orchestra at Carnegie HallA Year in Review  President Hsu's Instagram and X Accounts

Reviving Dead Real Estate Leads: Action Plan for Maximizing Client Opportunities(Want an "easy button" for growing your real estate database? Check out: http://BuildWithJosh.com)Go here to check out the full video replay here: https://youtu.be/nE40NWmi2DkIn this episode, we're diving into the essential strategies for reviving dead leads from your old database. Tune in as we discuss how to invigorate your conversations through emails, texts, and direct messages to generate more client opportunities. Inspired by successful agent James Brown, we explore a proven action plan to get the most out of your kvCORE database and beyond. Learn about fascinating metrics from the last 30 days, including lead generation stats, cost per lead, and conversion rates. Plus, discover useful scripts, templates, and interaction-based activities designed to maximize your opportunities during the selling season. Whether you're frustrated with tech overwhelm or looking for fresh ideas, this episode is loaded with actionable insights to help you thrive.Timestamps:00:00 Introduction to Reviving Dead Leads00:34 Inspiration and Background01:16 Action Plan Overview03:41 Lead Generation and Cost Analysis05:28 Lead Management Process10:20 Mathematics of Lead Conversion15:23 Cleaning Your Database19:31 Implementing the Action Plan26:21 Handling Ridiculous Replies27:27 Weekly Action Plan Overview28:31 Engaging with Leads28:59 Deal of the Week Strategy29:29 Friday Catch-Up and Bonus Tips30:29 Effective Communication Techniques32:01 Calculating Business Scenarios35:09 Collaborating with Lenders42:21 Using Video in Follow-Ups45:23 Final Q&A and Closing Remarks#exprealty #realtor #realestateagent #realtormarketing

Producer and long time Wu Tang Clan DJ Mathematics breaks down the creative process behind his new album Black Samson, the Bastard Swordsman. We also dive into why ranking hip hop whether playlists or all-time lists is so tough, with too many angles and no clear rules.Follow The Show:PatreonDiscordYoutubeInstagramX(Twitter)Follow Cipha Sounds:InstagramX(Twitter)TikTokFollow Rosenberg:InstagramX(Twitter)TIkTokThis podcast is sponsored by Monster Energy and Monster Music. Hosted on Acast. See acast.com/privacy for more information.

Episode: 3040 Leonardo and Borelli.  Today, two hemispheres come together.

One of the challenges facing faculty, staff, and administrators is keeping up with the continuous flow of email. In this episode, Robert Talbert joins us to discuss strategies to efficiently handle email so we can allocate time to other essential tasks.  Robert is a Professor of Mathematics at Grand Valley State University and the author of Flipped Learning: A Guide for Higher Education Faculty and a co-author of Grading for Growth: A Guide to Alternative Grading Practices that Promote Authentic Learning and Student Engagement in Higher Education. A transcript of this episode and show notes may be found at http://teaforteaching.com.

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Please enjoy this replay of episode 20 from November 2023.Coming to you from the California Mathematics Council - South annual conference, Sharona and Bosley sit down for a wonderful conversation with Dr. Sean Nank. Sean is an adjunct professor at California State University San Marcos, a full professor at the American College of Education, as well as a high school math teacher in the Oceanside Unified School District. Sean is also a recipient of the Persidential Award for Excellence in Mathematics and Science Teaching.In this incredible conversation, we talk with Sean about the human impact of assessments on our students and the important conversations that can be had once we really start to examine the impact of our grading systems. LinksPlease note - any books linked here are likely Amazon Associates links. Clicking on them and purchasing through them helps support the show. Thanks for your support!seannank.com How to Grade for Learning: Linking Grades to Standards, Ken O'ConnorResourcesThe Grading Conference - an annual, online conference exploring Alternative Grading in Higher Education & K-12.Some great resources to educate yourself about Alternative Grading:The Grading for Growth BlogThe Grading ConferenceThe Intentional Academia BlogRecommended Books on Alternative Grading (Please note - any books linked here are likely Amazon Associates links. Purchasing through them helps support the show. Thanks for your support!):Grading for Growth, by Robert Talbert and David ClarkSpecifications Grading, by Linda NilsenUndoing the Grade, by Jesse Stommel

Episode: 2579 Music and Mathematics.  Today, UH Math Professor Krešo Josić talks about music and mathematics.

This week on Diverse Thinking Different Learning, we welcome Dr. Aditya Nagrath. Dr. Nagrath is the founder of Elephant Learning Mathematics Academy and helps students overcome math anxiety, rapidly advancing their skills with just ten minutes of practice a few times a week. He holds a PhD in Mathematics and Computer Sciences and has over three decades of experience as a software engineer, entrepreneur, author, and speaker, working on a wide range of projects from atomic clocks to mobile apps.  Dr. Nagrath joins us for this episode to discuss mathematics anxiety - where it comes from, how it's misunderstood, how to address it and more. A child's early struggles with math are not always just academic but are also emotional and potentially even life-changing.  Dr. Nagrath draws from his rich background in math, computer science, and education to help us break down why so many students begin falling behind in math as early as kindergarten and how early delays often snowball into years of lost confidence, missed opportunities, and career shifts away from math-intensive fields. This isn't just about numbers or curriculum, however. As Dr. Nagrath explains, math anxiety is often rooted in beliefs such as “I'm not a math person” - beliefs that can trigger lifelong avoidance and reinforce themselves with every uncomfortable encounter with numbers. This is truly a vicious circle that hinders growth and learning well into adulthood. The conversation challenges the common misconception that disliking math is harmless. How early numeracy can actually influence language development, how adult comments can unconsciously pass limiting beliefs to children, and why literacy-focused initiatives may be unintentionally crowding out math readiness. Dr. Nagrath also tells us about Elephant Learning, a tech-based platform that adapts to each student's comprehension level and uses gamified learning to rebuild mathematical confidence from the ground up. This episode serves as a reminder that math isn't just a subject but a gateway and that what we do (or, for that matter, don't do) in the earliest years can shape far more than just test scores.   Show Notes: [2:22] - Dr. Aditya Nagrath explains how working with Elephant Learning revealed that minor complaints often mask deeper math anxiety. [5:05] - The belief that "I'm not a math person" stalls effort and future academic/career opportunities. [7:09] - Similar to AI training, learning depends on the meanings that we assign to experiences and challenges. [9:53] - Hear how Dr. Nagrath defines mathematics anxiety. [12:11] - Dr. Nagrath argues that many students' unresolved early math gaps snowball, derailing STEM careers and impacting the economy. [15:48] - Dr. Nagrath also asserts that Algebra is essential because it introduces written mathematics that are needed for interpreting the modern world. [17:40] - Hear how preschool math practice improves children's future reading, writing, and speaking abilities. [19:41] - Dr. Nagrath uses a basketball analogy to demonstrate that practicing math is essential because no alternative "game" exists. [21:46] - Dr. Nagrath explains that Elephant Learning builds math skills by meeting students at their comprehension level with gamified learning. [24:01] - By mapping standards to age levels, Elephant Learning helps students visualize progress. [27:18] - Because of deeply rooted self-doubt, overcoming math anxiety later in life tends to be more difficult. [28:44] - Dr. Nagrath stresses that problem-solving, like basketball, improves with practice rather than innate intelligence. [31:00] - Modern demands require deeper, language-like mathematical understanding. Links and Related Resources: Episode 59: What Is Dyscalculia (AKA Math Disorder)? with Monica Grillo Episode 60: A Multisensory Intervention for Kids Who Struggle with Math with Adrianne Meldrum Elephant Learning Elephant Learning - K-12 School Solutions Treating Mathematics Anxiety: Inclusive Strategies for Working with Students Exhibiting Mathematics Anxiety Connect with Us: Get on our Email List Book a Consultation Get Support and Connect with a ChildNEXUS Provider Register for Our Self-Paced Mini Courses: Support for Parents Who Have Children with ADHD, Anxiety, or Dyslexia Connect with Aditya Nagrath, PhD: Dr. Nagrath's LinkedIn Profile Email: anagrath@elephantheadsoft.com Phone: 303.919.6071

Dr. Shirley Madhere is a NYC-based plastic surgeon and Founder of Holistic Plastic Surgery.  This philosophy is based on a whole-body, mind, and spirit approach to beauty and incorporates wellness, integrative nutrition, functional aesthetics, and complementary medicine.   Dr. Madhere's approach to optimal outcomes in plastic surgery is through a lens of wellness, and is grounded in science and backed by ivy league medical study, research, and extensive surgical training.  View her menu of services at ElementsandGraces.com.  Consultations are available in-office, virtually, and online via Click-lift.com.   Coming soon: Dr. Madhere offers beauty on call services through Jet Set Beauty Rx, a mobile medical aesthetics unit delivering beauty in the privacy of your own home.  Reserve at JetSetBeautyRx.com.   As a creative outlet and means to broaden the perspective on the “spectrum of beauty,”  Dr. Madhere created Forever F.A.B., a podcast dedicated to Fashion, the Art of living well (i.e., wellness), and all things Beauty.  Visit ForeverFABpodcast.com for past and new episodes.     If you enjoy listening to the Forever F.A.B. podcast, get more audio and visuals with a membership through Patreon.  Choose the Gold, Platinum, or Diamond tier for premium added content, special co-hosts, lifestyle videos, branded merchandise, and private access to Dr. Shirley's Clubhouse by visiting patreon.com/ForeverFAB.   This week's podcast episode features an interview with Aisha Bowe.   Aisha Bowe is a Bahamian-American aerospace engineer, entrepreneur, and founder of a technology company.  She grew up in the United States in a working-class family. Her father immigrated from the Bahamas and was a taxi driver in Ann Arbor, Michigan.  Although her high school guidance counselor recommended that she become a cosmetologist, her father urged her to take a mathematics class at her local community college. That she excelled in math allowed her to transfer into engineering programs at the University of Michigan.  At the university, she completed her undergraduate degree in aerospace engineering in 2008, then earned a master's degree in space systems engineering in 2009.    Aisha worked at the Ames Research Center, a major NASA research center in the Flight Trajectory Dynamics and Controls Branch of the Aviation Systems Division.  She joined the Flight and Fluid Mechanics department and assisted in the development of algorithms in support of Air Traffic Management.  While at NASA, she also served as liaison to the Mathematics, Engineering, Science Achievement (MESA) Program, mentored students, held interview workshops and led NASA site tours.   Currently, Aisha is founder and CEO of STEMBoard, a company that solves technology challenges for government and private-sector clients.  She is also the creator of the LINGO coding kit which teaches hardware and software design.   Aisha's accolades are numerous and include: Entrepreneur of the Year by the Black Data Processing Associates (BDPA) of Washington, D.C. *INC 5000 2020 List of Fastest Growing Companies US Women's Chamber of Commerce “Emerging Star” Award *Silicon Valley's National Coalition of 100 Black Women's Women in Technology of the Year Award *NASA's Engineering Honor Award NASA Equal Employment Opportunity Medal   Aisha is an international speaker, entrepreneur, certified scuba diver, fashionista, and mountain climber.    Catch the latest episode of the Forever F.A.B. podcast on Apple podcasts, Spotify, YouTube, iheartradio, Podbean, and wherever you listen to your favorite podcasts.  For past episodes featuring guest star interviews, beauty product reviews and innovations in plastic surgery, visit ForeverFABpodcast.com.   Catch the latest episode of the Forever F.A.B. podcast on Apple podcasts, Spotify, YouTube, iheartradio, Podbean, and wherever you listen to your favorite podcasts.  For past episodes featuring guest star interviews, beauty product reviews and innovations in plastic surgery, visit ForeverFABpodcast.com. The F.A.B. Five according to Aisha Bowe: Let it go: sometimes a setback is a set up; Be intentional; Start a business that solves a problem you personally have; Fall in love with yourself; Invest early in yourself.   If you want to decode code or know someone who does, get your kit on stemlingo.com.   If you or your company are facing complex tech issues and want solutions “at the speed of mission,” visit stemboard.com.   Follow @Aisha Bowe on IG.    ***** As always, if you liked this episode of the Forever FAB podcast, please share it and subscribe to the feed. Listen to past episodes or check out who's coming up next on foreverfabpodcast.com.   Catch the latest episode of the Forever F.A.B. podcast on Apple podcasts, Spotify, YouTube, iheartradio, Podbean, and wherever you listen to your favorite podcasts.  For past episodes featuring guest star interviews, beauty product reviews and innovations in plastic surgery, visit ForeverFABpodcast.com.  To get more FAB, level up your listening and become a patron on patreon.com/foreverFAB.   For holistic beauty tips or to set up an appointment with me to discuss your personalized options for leveling up your beauty, go to ElementsandGraces.com and sign up for my newsletter or book a consultation—in-office or virtually.   For an online e-consultation on time, anytime and on your time, visit Click-Lift.com for your wellness, plastic surgery, and beauty questions on the go.   And… if you don't want to go anywhere or leave your home for your next Botox or filler injection, look out for Jet Set Beauty Rx offering aesthetic medical services such as injectable fillers and multi-vitamin facial treatments in a mobile medical unit.  Jet Set Beauty Rx is coming to your neighborhood soon.  Visit JetSetBeautyRx.com to reserve.    If you'd like to be a guest or know a potential FABulous guest for the Forever FAB podcast, let us know at foreverfabpodcast.com.   Produced by www.oneofoneproductions.com Recorded, mixed, edited and original music by www.23dbproductions.com   Podcast Medical Disclaimer The purpose of this podcast is to educate and inform. It is no substitute for professional care by your doctor or your own qualified healthcare professional. Never disregard professional medical advice or delay in seeking it because of something you have read on this podcast or in any linked materials. Guests who speak on this podcast express their own opinions, experience and conclusions, and Dr. Shirley Madhere neither endorses nor opposes any particular opinion discussed in this podcast. The views expressed on this podcast have no relation to those of any academic, hospital, practice, institution or other entity with which Dr. Shirley Madhere may be affiliated.

Patreon.com/thequestionshiphop questionshiphop.com Sean connects with Wu-Tang Clan's Mathematics for a "Can't Knock the Shuffle"-themed episode, powered by the AI in FYI.AI and covering the stories behind six randomly-selected Wu songs produced by Mathematics. They also talk about the latest Mathematics-produced Wu-Tang album 'Black Samson: The Bastard Swordsman.' Mathematics "Respect Mine" feat. Raekwon, Method Man, & Cappadonna (Love, Hell or Right, 2003) Wu-Tang Clan & Mathematics "Mandingo" (Black Samson, The Bastard Swordsman, 2025) Ghostface Killah "Mighty Healthy" (Supreme Clientele, 2000) Wu-Tang Clan "Do You Really (Thang Thang)" (The W, 2000) Method Man and Redman "Fire Ina Hole" (Blackout!, 1999) Wu-Tang Clan "Lesson Learn'd" (The Saga Continues, 2017) The Questions Hip-Hop: Instagram Sean Kantrowitz: Instagram Mathematics: Instagram

We have all had meaningful and profound encounters with beauty in our lives. Even though we often know what we mean when we say "That is absolutely beautiful," beauty, as it turns out, is not easy to articulate in words. It goes far beyond outward or aesthetically pleasing appearances. There is much more theological depth and complexity to the topic of beauty than what may be "in the eye of the beholder."  Our guest this week and next on the Profile is Miss Paige Lehrmann, friend of Watchman Fellowship, Christian apologist, youth leader, and math professor. We'll be discussing Paige's insights about the nature of beauty and how it points us to Christ. Paige Lehrmann is the Director of Student Ministries at St. Andrew's Community Church in Oklahoma City and a student at Dallas Theological Seminary. She earned her B.A. in Philosophy and Mathematics from Oklahoma Baptist University, where she completed an interdisciplinary thesis on the Trinity. Paige went on to pursue graduate studies in mathematics at the University of Oklahoma and has taught as an adjunct professor at Mid-America Christian University. She has presented at apologetics conferences on topics such as the Trinity, the divinity of Christ, and theistic arguments from beauty. Through her work, she hopes to help others think deeply about faith, truth, and the beauty of the Gospel.You may contact Paige via email at Paige.lehrmann@gmail.com. Free Resources from Watchman Fellowship Atheist New Testament scholar Dr. Bart D. Ehrman: www.watchman.org/Ehrman  Atheism: www.watchman.org/Atheism  Latter-day Saints: www.watchman.org/Mormonism Panpsychism: https://www.watchman.org/files/ProfilePanpsychism.pdf The New Age Movement: https://www.watchman.org/profiles/pdf/newageprofile.pdf Additional ResourcesFREE: We are also offering a subscription to our 4-page bimonthly Profiles here: www.watchman.org/FreePROFILE NOTEBOOK: Order the complete collection of Watchman Fellowship Profiles (around 700 pages -- from Astrology to Zen Buddhism) in either printed or PDF formats here: www.watchman.org/NotebookSUPPORT: Help us create more content like this. Make a tax-deductible donation here: www.watchman.org/GiveApologetics Profile is a ministry of Watchman Fellowship For more information, visit www.watchman.org © 2025 Watchman Fellowship, Inc.

Sam Clausen, upper school mathematics teacher at Atlanta Classical Academy in Atlanta, Georgia, delivers a lecture on how to use discussion as a tool in mathematics instruction. This lecture was given at the Hoogland Center for Teacher Excellence seminar, “The Art of Teaching: Mathematics” in October 2024. The Hoogland Center for Teacher Excellence, an outreach of the Hillsdale College K-12 Education Office, offers educators the opportunity to deepen their content knowledge and refine their skills in the classroom.See omnystudio.com/listener for privacy information.

For Descartes body is purely geometrical. So how does he understand features we can perceive, like color, and causation between bodies?