'Will my bacon sandwich kill me?', 'Is vaping better than smoking?', 'How do you become an astronaut?' - just some of the Big Questions we ask some of the brightest minds behind Oxford science. Join us in each podcast as we explore a different area of science.
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Mathematics Podcasts
The National Council of Teachers of Mathematics (NCTM) welcomes you to Adding It All Up —a podcast created by and for mathematics educators and teachers. Join us each month as we explore current topics, insights, and emerging trends with thought leaders in the math community.
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Host Russ Altman, a professor of bioengineering, genetics, and medicine at Stanford, is your guide to the latest science and engineering breakthroughs. Join Russ and his guests as they explore cutting-edge advances that are shaping the future of everything from AI to health and renewable energy. Along the way, “The Future of Everything” delves into ethical implications to give listeners a well-rounded understanding of how new technologies and discoveries will impact society. Whether you’re a ...
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IDEAS is a place for people who like to think. If you value deep conversation and unexpected reveals, this show is for you. From the roots and rise of authoritarianism to near-death experiences to the history of toilets, no topic is off-limits. Hosted by Nahlah Ayed, we’re home to immersive documentaries and fascinating interviews with some of the most consequential thinkers of our time. With an award-winning team, our podcast has proud roots in its 60-year history with CBC Radio, exploring ...
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History of mathematics research with iconoclastic madcap twists
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This podcast is about Science, Technology, Engineering, Mathematics, Music, Philosophy, Culture, Graduate life and much more.
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This podcast is a channel on the New Books Network. The New Books Network is an academic audio library dedicated to public education. In each episode you will hear scholars discuss their recently published research with another expert in their field. Discover our 150+ channels and browse our 28,000+ episodes on our website: newbooksnetwork.com Subscribe to our free weekly Substack newsletter to get informative, engaging content straight to your inbox: https://newbooksnetwork.substack.com/ Fo ...
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NCSM Leadership in Mathematics Education Learning with Leaders
NCSM Leadership in Mathematics Education
NCSM's Leadership in Mathematics Education Podcasts are published as part of the educational services NCSM provides members and visitors to the NCSM website -- http://mathedleadership.org NCSM - Where Mathematics Leaders Go To Learn
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Interviews with mathematics education researchers about recent studies. Hosted by Samuel Otten, University of Missouri. www.mathedpodcast.com Produced by Fibre Studios
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Conversations, explorations, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.
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Philosophy in the real world. Interviewing intellectuals across the globe. Grappling with the biggest ideas. stevepatterson.substack.com
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Periodic audiocasts from American Scientist, a publication of Sigma Xi, The Scientific Honor Society.
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Conversations about science, technology, history, philosophy and the nature of intelligence, consciousness, love, and power. Lex is an AI researcher at MIT and beyond.
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Insights and interviews from the Mathematics Faculty, University of Cambridge. Voices of Mathematics takes you inside the University of Cambridge's Mathematics Faculty, the home of the Cambridge Mathematics departments. From number theory and geometry to cosmology and quantum physics, the Faculty's work explores fundamental and exciting questions to extend the boundaries of discovery. In conversations with researchers from both departments, we explore topics across pure and applied mathemati ...
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Maths is often dreaded as a subject by most of the students. Here is an attempt to simplify various topics in Mathematics and help reduce Maths Phobia.
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Welcome to Science Sessions, the PNAS podcast program. Listen to brief conversations with cutting-edge researchers, Academy members, and policymakers as they discuss topics relevant to today's scientific community. Learn the behind-the-scenes story of work published in PNAS, plus a broad range of scientific news about discoveries that affect the world around us.
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Intellectually Curious is a podcast by Mike Breault featuring over 1,400 AI-powered explorations across science, mathematics, philosophy, and personal growth. Each short-form episode is generated, refined, and published with the help of large language models—turning curiosity into an ongoing audio encyclopedia. Designed for anyone who loves learning, it offers quick dives into everything from combinatorics and cryptography to systems thinking and psychology. Inspiration for this podcast: "Mu ...
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Mathematically Uncensored
Center for Minorities in the Mathematical Sciences, Dr. Aris Winger, Dr. Pamela E. Harris
Talk that is real and complex, but never discrete.
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Podcasts from the Mathematical Institute, part of the Maths, Physical and Life Sciences Division
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Custom Posts - Blip - Blip
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The following podcasts look at linear systems and the equation of a line
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Join mathematician Professor Hannah Fry and science creator Michael Stevens (Vsauce) as they dig into the weird scientific questions that often go unexplored. Welcome to The Rest Is Science, a show that sits in the fascinating space between what we think we know, and what we actually know. Why do we assume we understand things like time, randomness, or even gravity? Once you start questioning these familiar ideas, reality becomes astonishingly strange and completely fragile. Whether you're a ...
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NonTrivial is a podcast about the patterns that exist at the intersection of science, philosophy and complexity, and how these speak to universal principles related to skills, growth and life. The longer you listen, the more you’ll internalize these universal principles and see how they inform your work, your ideas, and the way you shape the world around you. Become a Member at nontrivialpodcast.com or patreon.com/8431143/join Premium members get access to Techniques and Mindsets videos, whe ...
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Peter Adamson, Professor of Philosophy at the LMU in Munich and at King's College London, takes listeners through the history of philosophy, "without any gaps". www.historyofphilosophy.net
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The story of technological progress is one of drama and intrigue, sudden insight and plain hard work. Let’s explore technology’s spectacular failures and many magnificent success stories. This content is in service of Houston Public Media’s education mission and is sponsored by the University of Houston. It is not a product of our news team.
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Explore history's most intriguing stories, people, places, events, and mysteries, delivered in a supremely calming atmosphere. If you struggle to fall asleep and you have a curious mind, Sleepy History is the perfect bedtime companion. Our stories will gently grasp your attention, pulling your mind away from any racing thoughts, making room for the soothing music and calming narration to guide you into a peaceful sleep. Sleepy History is a production of Slumber Studios. To learn more, visit ...
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We believe that when people think historically, they are engaging in a disciplined way of thinking about the world and its past. We believe it gives thinkers a knack for recognizing nonsense; and that it cultivates not only intellectual curiosity and rigor, but also intellectual humility. Join Al Zambone, author of Daniel Morgan: A Revolutionary Life, as he talks with historians and other professionals who cultivate the craft of historical thinking.
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Room to Grow is the math podcast that brings you discussions on trending topics in math education in short segments. We’re not here to talk at people. We’re here to think and learn with others — because when it comes to mathematics there’s always room to grow!
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This podcast features interviews with educators, leaders and even students in relation to maths education.
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Exploring strategies and tool moving towards metis-rich instruction, successfully guiding students as they struggle to achieve understanding of the complexities of mathematics.
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This is Mathematical basis for reality; a podcast to fill the void.
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Professor of Mathematics Marcus du Sautoy reveals the personalities behind the calculations and argues that mathematics is the driving force behind modern science.
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Mathematics - in a great school close to home!
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51
Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
Sean Carroll | Wondery
Ever wanted to know how music affects your brain, what quantum mechanics really is, or how black holes work? Do you wonder why you get emotional each time you see a certain movie, or how on earth video games are designed? Then you’ve come to the right place. Each week, Sean Carroll will host conversations with some of the most interesting thinkers in the world. From neuroscientists and engineers to authors and television producers, Sean and his guests talk about the biggest ideas in science, ...
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Hello!! My podcast will be about mathematics. The math that I will talk about is math 2 with the integrated mathematics textbook and work book. I will go over chapters 1-11 in this podcast.
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Why is mathematics so hard? Here, we talk about the foundations for whole numbers and fractions and suggest that math can be natural and fun to us! Cover art photo provided by naomi tamar on Unsplash: https://unsplash.com/@naomitamar
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The TODOS: Mathematics for ALL Podcast explores the intersection of mathematics education, social justice, and identity. Season 4 brings in new hosts, Theodore Chao and Shari Kaku, to amplify the voices of educators, activists, and community leaders who challenge traditional norms and reimagining math education as an inclusive and humanizing practice. Season 4 focuses Invisibility & Hypervisibility in Mathematics Education: An Exploration of Asian American and Pacific Islander Mathematics Id ...
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Today, we will answer the life long question... "When will I ever use this math when I grow up?"
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Lesson by lesson podcasts for teachers of Illustrative Mathematics®. (Based on IM 9-12 Math™ by Illustrative Mathematics®, available at www.illustrativemathematics.org.)
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The Human Action Podcast features in-depth interviews on current topics in economics through an Austro libertarian lens.
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Jeremiah Joven Joaquin and James Franklin eds., "The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability" (Bloomsbury, 2025)
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55:15The 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 …
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51
Why spirituality is central to Indigenous mathematics
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54:08Indigenous 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…
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Welcome to Voices of Mathematics, a podcast from the Mathematics Faculty at the University of Cambridge. In this episode, we revisit one of our favourite interviews from the last year with Professor Hannah Fry. In January 2025 mathematician, author and broadcaster Hannah Fry joined the Department of Applied Mathematics and Theoretical Physics as Ca…
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Bob uses clips from his recent interview with Eric Weinstein to explain why Weinstein thinks gauge theory can fix how economists measure the cost of living, unify competing price indices, and handle changing preferences over time, and why Austrians shouldn’t dismiss him as a crank. He summarizes Eric’s claim that standard mathematical economics rel…
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Circle and Proportion: Gibbs, the Radcliffe Camera, and the Mathematics of a Masterpiece
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5:02A deep dive into how James Gibbs turned a radical circular library into England’s first, using precise geometric rules drawn from his own Rules for Drawing. We explore the 1:10 column proportion, the one-fifth entablature, and the pedestal adjustments Gibbs justified by decorum, showing how he balanced exacting math with artistic judgment. From the…
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Episode116-Jenn Malue Bartone, "Hidden Brilliance: What We Miss When We Reduce ADHD to a Label
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52:48Episode116-Jenn Malue Bartone, "Hidden Brilliance: What We Miss When We Reduce ADHD to a Label"By NCSM Leadership in Mathematics Education
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How did pages of mysterious “gibberish” sent from Madras find their way to one of Cambridge University’s most respected mathematicians? Were the strange formulas the work of a deluded mind - or breakthrough insights of an unknown genius? The author of that letter was Srinivasa Ramanujan. His story inspired two Hollywood blockbusters (Goodwill Hunti…
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Vector: Robyn Arianrohd on the Surprising Story of Space, Time, and Mathematical Transformation
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33:06On October 16, 1843, William Rowan Hamilton was taking a walk with his wife Helen. He was on his way to preside over a meeting of the Royal Irish Academy. As Hamilton came to Broome Bridge, over the Royal Canal, the solution to a vexing problem finally emerged in front of him. He was so excited, and perhaps so afraid that he might forget, that he p…
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Revealing facts about the Christmas song meant for Easter
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54:08Handel’s Messiah is one of the best-loved pieces of Christmas music. Only it was meant for Easter. But it draws on far more from the Old Testament than the New. There are more surprising facts about this 18th-century masterpiece that IDEAS explores with Ivars Taurins, founding director of the Tafelmusik Chamber Choir who has conducted Messiah over …
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The Engines of Our Ingenuity 2817: Creativity
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3:49Episode: 2817 Where do creative ideas come from? Today, let's talk about creativity.By Dr. Krešimir Josić
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An apocalyptic retelling of the Christmas story
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54:07The nativity story that Christians believe is that God took the form of a baby named Jesus who was born to save the world and bring about an enduring peace. So what happened? Did we miss it? And what happens next? These are questions Trappist monk Thomas Merton grappled with in his own meditation on the Christmas story. His version "The Time of The…
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We dive into CSS Grid Lanes—the native masonry solution that moves items into the shortest available column, eliminating the need for heavy JavaScript. Learn how it differs from standard Grid, the three-line setup (display: grid lanes; grid template columns; gap), and how tolerance affects placement for accessibility. Explore real-world use cases, …
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Tiny Fossils, Big Shifts: 2025 Breakthroughs in Fossil Fish Evolution
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4:58A deep-dive into 2025 discoveries that rewrite the roots of modern fishes. With high-tech imaging and modeling, these tiny fossils are expanding our view of the grand history of vertebrate evolution. Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information. Sponsored by Embersilk LLC…
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Rényi’s Parking Problem and the 0.7475979 Limit Behind AI
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4:45We dive into Alfred Rényi's 1958 random sequential parking puzzle on a line, uncovering the jamming limit and the famous parking constant ≈ 0.7475979. We explore how this one-dimensional geometric bound mirrors how tokens fill context in transformers, via causal attention masking and the idea of metastable anchor points (Rényi centers) that boost e…
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Lady Frances Berkeley/Amy Stallings: Bacon’s Rebellion, Colonial Virginia, and First-person Historical Interpretation
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31:18In this episode of Historically Thinking, we begin not with a historian’s voice, but with the voice of a seventeenth-century woman. Lady Frances Culpeper Berkeley—born in England, twice widowed, and married in 1670 to Sir William Berkeley, governor of Virginia—speaks from the midst of crisis. Jamestown has burned. Nathaniel Bacon’s rebellion has fr…
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The Engines of Our Ingenuity 2834: Wombs and Witchcraft
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3:51Episode: 2834 Wombs and Witchcraft: Edward Jorden's Suffocation of the Mother (1603). Today, wombs and witchcraft.By Richard H. Armstrong
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Could Santa Clause still exist IF we stripped away the magic? If the ability to bend spacetime was gone? What conditions would Santa need to deliver a present to every human being on Earth in a single night? Hannah Fry and Michael Stevens explore the historical, geographical, and logistical realities behind these questions using population data, lo…
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Where to find 'critical hope' in hard times
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54:09In an era of political polarization and fatigue from ongoing crises, hope is critical. But it's not something you have; it's something you do, argues education scholar Kari Grain. "Critical hope" in action is not just the belief that transformation is possible — it's necessary. In her book, she explores seven principles for practicing hope that con…
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Fomalhaut Unleashed: The Great Eye, Debris Disks, and a Cosmic Collision Playground
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4:40A tour of the young star Fomalhaut and its spectacular, collision-prone debris disk. We unravel why its bright ring behaves like a nonstop demolition derby, the misidentified exoplanet Dagon, and the rare feature of two stellar companions each hosting a disk. It's a dynamic, real-world lab showing how chaos fuels planet formation in a multi-star sy…
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The Critical 3%: Making Software Feel Instant with Dean and Ghemawat
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5:03A practical dive into performance engineering—how estimation, the latency hierarchy, and smart data structures turn frustrating delays into instant responses. Guided by Jeff Dean and Sanjay Ghemawat's performance hints, we unpack moving from O(n log n) to O(n), hoisting temporaries, and fast paths for the common case. We also glimpse real-world win…
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Fisher Information: The Sharp Curve Behind What Data Reveals
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5:22In this deep-dive, we explore how Fisher Information measures how much your data can tell you about an unknown parameter. Visualize it through the curvature of the log-likelihood—sharp curves mean high information and precise estimates, flat curves mean ambiguity. We’ll cover additivity across independent observations, the Cramér–Rao bound as the u…
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Holiday Message 2025 | The Romance of the University
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42:50Time for the holiday message! Rounding off the year with a brief and casual reflection on some issue that doesn't quite rise to the level of a full solo podcast. And hopefully something uplifting. This year, I offer a short apologia for higher education in the liberal arts and sciences, focusing not on the down-to-earth economic/occupational benefi…
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The Engines of Our Ingenuity 1495: The Chauffer Problem
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3:38Episode: 1495 The new technological elite: chauffeurs then, computer experts today. Today, we learn to drive our own cars -- and manage our own computers.By Dr. John Lienhard
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From their opulent rise in 19th-century Paris and London to their golden age in bustling American cities, department stores revolutionized shopping and shaped modern consumer culture. These grand spaces weren’t just for buying...they were places of wonder, luxury, and social change. Tonight, explore the evolution, charm, and cultural legacy of depa…
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Episode 2511: Mario Sánchez Aguilar - math ed research in Latin America
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26:21Mario Sánchez Aguilar from the National Polytechnical Institute in Mexico City, Mexico, discusses the article, "Latin American research on mathematics education: A narrative review" and the accompanying special issue in ZDM Mathematics Education (Volume 57). Co-authors: Marcelo de Carvalho and Jhony Alexander Villa-Ochoa Article URL: https://link.s…
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The Dead Fish Pitch: Debunking Baseball's Slow-Motion Strategy
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4:48A data-driven dive into the Eephus pitch—the infamous 'dead fish'—exploring its history, the physics behind a slow, high-spin arc, and what the data really says about contact quality, exit velocity, and on-base percentage. We separate myth from method, examine why this oddball pitch persists, and discuss how teams might use it as a legitimate tool …
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Geometry in Chaos: Vorticity, Vortex Stretching, and the Hidden Order of Turbulence
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5:31From a creek’s tiny whirl to the robust math of fluids, we explore how vorticity and vortex stretching power turbulent flows. We trace Berger’s vortex as a stable exact solution, then reveal high‑resolution simulations showing that, in the inviscid 3D Euler equations, the anticipated blow‑up is tamed by dynamic depletion: vortex tubes flattening in…
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Gabriel's Horn: Finite Volume, Infinite Surface
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4:52A deep dive into Torricelli's trumpet, the shape formed by revolving y = 1/x about the x-axis from x = 1 to infinity. We explore why its volume is finite (π) even as its surface area diverges to infinity, unravel the painter's paradox, and see how calculus resolves the mystery. We'll also discuss why the paradox disappears in the real world due to …
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Petra and the Desert Empire: How the Nabataeans Built a Trading Power
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4:33In this episode we explore how the Nabataeans turned Petra, a rose-red rock city, into the heart of a powerful trading kingdom. Learn how ingenious water engineering, control of the incense route from Yemen to Gaza, and fierce defense allowed them to dominate ancient trade, withstand big rivals, and endure as a commercial force even after Rome clai…
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The Seahorse Emoji Signal: How AI's Self-Correction Shapes the Next-Gen Models
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4:41We unpack a provocative claim: a tiny, non-existent seahorse emoji as a tripwire revealing a new phase in AI training—the use of thinking-trace data that exposes the model's internal problem-solving process. We trace how labs feed rough drafts into models to produce more stable, better-aligned AI, and what this means for reliability across closed a…
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The Engines of Our Ingenuity 1494: X-Ray Hair Removal
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3:38Episode: 1494 The strange persistence of X-ray hair removal. Today, we kill ourselves to remove hair.By Dr. John Lienhard
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Emil Grosswald: From Refugee Odyssey to a Pillar of Number Theory
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5:21An intimate journey through the life of Emil Grosswald, a towering figure in number theory who thrived under upheaval. From dual degrees in mathematics and electrical engineering in Bucharest, through wartime flight across Europe to Cuba, and finally to a transformative U.S. career under Hans Rademacher, Grosswald bridged pure theory and practical …
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RLVR, Ghosts, and Vibe Coding: Karpathy’s 2025 LLM Year in Review
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5:41A deep dive into the foundational shifts Karpathy highlights for 2025: reinforcement learning from verifiable rewards (RLVR) driving massive cheap optimization, the rise of ‘thinking time’ traces and jagged, task-optimized intelligence, and the birth of vibe coding—guiding powerful AI with plain language. We explore the new LLM app layer that turns…
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Shining a Light on the AI Black Box: Chain of Thought and Monitorability
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5:13We explore how monitoring AI reasoning can reveal safety signals in critical decisions. Learn what monitorability means, why a perfect transcript isn’t required, and how robust metrics and three evaluation modes—intervention, process, and outcome—help catch red flags. The episode covers why bigger models aren’t necessarily less transparent, the sur…
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Shendi Take One: Asia's Deepest Onshore Well Reaches 10,910 Meters
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5:02We distill CNPC's Shendi Take One Well in the Taklamakan Desert—a 10,910-meter onshore drilling milestone that makes Asia’s deepest vertical well and ranks second globally behind the Kola borehole. Drilled from May 2023 to February 2025, it set a world record for the fastest onshore depth to that level and yielded the first ultra-deep onshore oil-a…
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The Siberian Snowman: A 14-Mile Line of Arctic Lakes From Space
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4:37NASA’s Earth Observatory spotlights a surreal 22-kilometer chain of five pale-blue thermokarst lakes near Billings on Russia’s Chukchi Peninsula. The pattern isn’t surface snow but underground ice wedges melting in summer, causing the ground to slump into a line that winds and waves slowly align end-to-end. From orbit you can see this dramatic natu…
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The Engines of Our Ingenuity 1492: Necessity in the Siege of Paris
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3:36Episode: 1492 Necessity and invention during the 1870 siege of Paris. Today, necessity, invention, and the Siege of Paris.By Dr. John Lienhard
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DisCIPL: MIT CSAIL’s Two-Role AI for Collaborative Reasoning
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4:24We dive into DisCIPL (Decentralized Collaborative Intelligent Planning Language model), a two-part framework that splits reasoning into a planner LM that writes a task-specific program and a swarm of cheap follower LMs that execute in parallel. The planner acts as a blueprint-writer and gatekeeper, guiding thousands of quick, inexpensive attempts a…
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Chain of Responsibility: Decoupling Handlers for Flexible Software
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5:04From button taps on your iPhone to complex event flows, this episode breaks down the Chain of Responsibility design pattern. Learn how a chain of handlers can decide who processes a request at runtime, keeping senders agnostic of receivers and enabling dynamic, extensible systems. We’ll look at Cocoa’s responder chain as a concrete example, discuss…
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Spherical Voronoi Unveiled: Real-Time Photorealism Without Neural Giants
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5:07We dive into Spherical Voronoi (SV), a new framework that partitions viewing directions on the sphere with adaptive Voronoi cells to capture sharp reflections and high-frequency lighting in real-time rendering. See how SV uses a single softmax temperature to smoothly span diffuse to mirror-like highlights, outperforming traditional approaches like …
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Microbes are awesome, says biologist Paula Welander. They have shaped Earth’s chemistry and its environment over billions of years, including oxygenating the planet to make it habitable for larger life forms. In turn, microbes have been shaped by that very same environment, evolving as the climate has evolved, she says. Welander now studies the lip…
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Episode: 1491 In which business schools study a leaderless orchestra. Today, we have no leader.By Dr. John Lienhard
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51
How 'body horror' helps us confront the fears within us
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54:08"We are the monsters" — that's the premise for the genre of film known as body horror — movies that fixate on monstrous and grotesque changes to the body. There have been good body horror films and bad ones, but "The Fly" starring Jeff Goldblum and Geena Davis was perhaps the most consequential. The movie captured anxieties around bodily autonomy a…
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Letterlock: From Spiral Seals to Virtual Unfolding
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4:38Dive into the ancient art of letterlocking—the craft of folding a letter into its own secure envelope. We trace spiral locks, self-destruct mechanisms, and the long arc from Mesopotamian seals to modern physical information security. Then see how X-ray microtomography lets researchers virtually unfold 300-year-old letters from the Brienne Collectio…
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Aerographite: The Ultra-Light, Ultra-Conductive Carbon Aerogel
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4:57We dive into aerogels and the extreme aerographite—a nanoscale, three‑dimensional carbon network so light it weighs less than 0.2 mg per cubic centimeter, yet conducts electricity even at cryogenic temperatures. Learn how a sacrificial zinc oxide template and chemical vapor deposition create this porous, conductive marvel, why its vast internal sur…
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The Engines of Our Ingenuity 2547: Charging Interest
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3:49Episode: 2547 Changing views on charging interest throughout history. Today, interest.By Dr. Andy Boyd
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Tucked away in old engineering kits and museum drawers is a device whose sweeping motion once captivated mathematicians and designers alike. The ellipsograph: a mechanical tool built from sliding arms and rotating joints that were tracing flawless curves long before computers made such things effortless. While they have the appearance of an ancient…
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51
How to change minds and find common ground
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54:09In 2024, 'polarization' was Merriam-Webster's word of the year. That division still grows, making it increasingly difficult to connect to one another. But there are people having important conversations and they have advice for us all. From fighting for LGBTQ+ rights in Colombia, championing human rights in Southern Africa and working for a two-sta…
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Pulsar Planets: Diamonds from the Ashes of Stars
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4:38Discover how the first confirmed exoplanets didn’t orbit a sunlike star but a pulsar, the ultra-dense remnant of a supernova. We unpack pulsar timing—the cosmic clockwork that reveals planets by tiny shifts in pulse arrival times—and explain how these worlds can form from the star's shredded debris, sometimes as carbon-rich, 'diamond' planets. We'l…
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