Breaking Math Podcast

Mathematician, mental-math performer, and backgammon grandmaster Arthur Benjamin joins Noah and Autumn to talk about his book How to Win. Together they explore what mathematics knows about winning that human intuition gets wrong: coincidences, the birthday paradox, gambler's ruin, and why the house wins even when you reach your goal more than half the time.Timeline:00:00 Can math ruin the fun of games?00:38 Why people play for the challenge, not the answer02:35 Mental arithmetic and the human element03:30 Calculators, AI, and the future of coding05:47 What does math know about winning that intuition gets wrong?06:02 Coincidences and the birthday paradox10:16 Why games are a microcosm for pattern-seeking16:40 What games teach that the classroom doesn't16:52 Gambler's ruin: how to get to the concert20:30 The paradox: why casinos aren't afraid22:30 What does "winning" really mean?23:29 Wordle streaks vs. average guesses27:07 Rubik's Cube, blackjack, and why some games never get old35:38 Does math take the mystery out of games? Follow Arthur Benjamin on his website:(https://www.arthurbenjamin.info/)Subscribe for more on math, AI, technology, and the systems running the world. Follow Breaking Math onSubstack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Bluesky (https://bsky.app/profile/breakingmath.bsky.social)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)Follow Autumn onX (https://x.com/1autumn_leaf)Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social)Instagram (https://www.instagram.com/1autumnleaf/)Substack (https://substack.com/@1autumnleaf)email: [email protected]

"I'm just not a math person." If you've ever said that about yourself, this episode is for you.Dr. Geillan Aly, author of Compassionate Math, joins Breaking Math to break down the real difference between math anxiety and math trauma — and why mathematics, more than almost any other subject, is uniquely built to make one bad experience feel like permanent proof of failure.In this episode we cover: 00:00 – What is math trauma, and why is it different from anxiety? 02:35 – Why math specifically (vs. history, reading, or other subjects)? 07:28 – Teaching concepts vs. teaching procedures 13:32 – The "sixes" story: a failing student's transformative breakthrough 20:15 – Math anxiety vs. math trauma, explained 28:56 – Whose fault is math trauma — students, teachers, or society? 36:21 – How compassionate math scales beyond the classroom 39:21 – One piece of advice for students, and one for teachersFollow Geillan Aly on her website:(https://www.compassionatemath.com/) Subscribe for more on math, AI, technology, and the systems running the world. Follow Breaking Math onSubstack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Bluesky (https://bsky.app/profile/breakingmath.bsky.social)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)Follow Autumn onX (https://x.com/1autumn_leaf)Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social)Instagram (https://www.instagram.com/1autumnleaf/)Substack (https://substack.com/@1autumnleaf)email: [email protected]

Professional forecaster Molly Hickman breaks down what it really means to assign a probability to the future — and why she believes generalists often out-forecast subject-matter experts. This episode explores the art and science of forecasting, from techniques to ethical considerations, and how AI and prediction markets are shaping our understanding of the future.Key TopicsThe definition of forecasting and its importanceTechniques for starting in forecastingThe role of AI and large language models in forecastingHow to interpret probabilities and conditional forecastsForecasting in complex systems like climate and geopoliticsEthical boundaries and red lines in prediction marketsThe impact of AI bots on forecasting accuracy and decision makingChapters03:06 Getting Started with Forecasting: Tools and Techniques06:15 Beginning Forecasting as a Beginner07:31 Gut Feelings vs Market Wisdom08:33 The Delphi Loop and Group Forecasting09:39 Measuring Forecast Accuracy and Skill11:17 Forecasting Long-Term and Uncertain Events12:40 Extrapolating Trends and Model Limitations14:19 AI Bots in Forecasting and Their Performance18:16 Prediction Markets as Collective Wisdom19:19 The Future of Prediction Markets and Society24:06 The Meaning of Probabilities and Risk Assessment27:20 Dealing with Chaos and Unpredictability32:52 Combining Models and Expert Opinions36:31 Forecasting and Expertise in Science and Policy39:01 Forecasting AI Risks and Ethical BoundariesFollow Molly Hickman on X (https://x.com/celloMolly)Follow Breaking Math onSubstack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)Follow Autumn onX (https://x.com/1autumn_leaf)Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social)Instagram (https://www.instagram.com/1autumnleaf/)Substack (https://substack.com/@1autumnleaf)email: [email protected]

What does it mean to be alive? In this episode of Breaking Math, Autumn and Noah speak with Melanie Challenger, author of Alive, about one of the most profound questions in science and philosophy: how do we define life?Challenger argues that life is not simply a machine-like process or a bundle of genetic instructions. Living beings are embodied, purposeful agents. From single-celled organisms to sequoia seeds, from animals to human beings, life is marked by an astonishing capacity to work to keep itself alive.Chapters08:12 The concept of purpose in living beings09:14 The scientific view of purpose and agency11:52 The importance of purpose and meaning in life13:19 The danger of ignoring organism agency in science14:34 Living beings as purposeful agents15:35 Comparing purpose in a Roomba and a single-celled organism18:03 Autopoetic vs allopoetic systems20:03 Free will, agency, and the universe23:24 The physical basis of life and energy28:38 Aristotle's concept of psyche and purpose33:46 The importance of understanding what life truly is37:56 Material integration and the difference between machines and living beings38:15 The concept of self and embodiment in life41:09 The whole body as the agent, not just the brainFollow Melanie Challenger on her website:(https://www.melaniechallenger.com/) Subscribe for more on math, AI, technology, and the systems running the world. Follow Breaking Math onSubstack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Bluesky (https://bsky.app/profile/breakingmath.bsky.social)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)Follow Autumn onX (https://x.com/1autumn_leaf)Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social)Instagram (https://www.instagram.com/1autumnleaf/)Substack (https://substack.com/@1autumnleaf)email: [email protected]

Neuroscientist Stuart Firestein (Columbia University) joins Breaking Math to make an extravagant claim: uncertainty isn't a weakness in science — it's the defining feature that makes progress possible. In this episode, we break down why the "one right answer" myth is one of the most damaging ideas in science, why real experts are often the most uncertain people in the room, and why authority and expertise pull in opposite directions, covering two fundamentally different kinds of probability, why Darwin never erased a 300-year-old classification system built on an assumption he disproved, why AI is exceptional at prediction but not built for causation, and why pseudoscience always has a confident answer while real science rarely does — plus the philosophical difference between hope and optimism, and why Voltaire had to invent the word "optimism" in 1759 to describe it. Chapters03:00 Predictability and the sea of uncertainties04:08 Science as a search for probabilities and multiple solutions06:16 Biological classification and the dynamic nature of species09:10 The optimistic view of a branching universe12:41 Probability as the language of optimism16:48 Two types of probability and their roles17:50 AI, probabilistic models, and the future of certainty21:40 Science and the creation of better ignorance23:21 The importance of asking questions over giving answers27:21 Authority versus knowledge in science30:04 Pluralism and multiple solutions in science32:46 Science in the gray area of uncertainty35:39 The brain and randomness in thought39:44 Science as a source of hope and optimismFollow Breaking Math onSubstack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Bluesky (https://bsky.app/profile/breakingmath.bsky.social)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)Follow Autumn onX (https://x.com/1autumn_leaf)Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social)Instagram (https://www.instagram.com/1autumnleaf/)Substack (https://substack.com/@1autumnleaf)email: [email protected]