Breaking Math Podcast

Breaking Math Podcast

di Autumn Phaneuf & Noah Giansiracusa
MatematicaScienze naturali
Stagione 3
31: Into the Abyss (Part Two; Black Holes)
Black holes are objects that seem exotic to us because they have properties that boggle our comparatively mild-mannered minds. These are objects that light cannot escape from, yet glow with the energy they have captured until they evaporate out all of their mass. They thus have temperature, but Einstein's general theory of relativity predicts a paradoxically smooth form. And perhaps most mind-boggling of all, it seems at first glance that they have the ability to erase information. So what is black hole thermodynamics? How does it interact with the fabric of space? And what are virtual particles?
S3 · E31
23 ago 2018
56:49
30: The Abyss (Part One; Black Holes)
The idea of something that is inescapable, at first glance, seems to violate our sense of freedom. This sense of freedom, for many, seems so intrinsic to our way of seeing the universe that it seems as though such an idea would only beget horror in the human mind. And black holes, being objects from which not even light can escape, for many do beget that same existential horror. But these objects are not exotic: they form regularly in our universe, and their role in the intricate web of existence that is our universe is as valid as the laws that result in our own humanity. So what are black holes? How can they have information? And how does this relate to the edge of the universe?
S3 · E30
2 ago 2018
51:09
29: War
In the United States, the fourth of July is celebrated as a national holiday, where the focus of that holiday is the war that had the end effect of ending England’s colonial influence over the American colonies. To that end, we are here to talk about war, and how it has been influenced by mathematics and mathematicians. The brutality of war and the ingenuity of war seem to stand at stark odds to one another, as one begets temporary chaos and the other represents lasting accomplishment in the sciences. Leonardo da Vinci, one of the greatest western minds, thought war was an illness, but worked on war machines. Feynman and Von Neumann held similar views, as have many over time; part of being human is being intrigued and disgusted by war, which is something we have to be aware of as a species. So what is warfare? What have we learned from refining its practice? And why do we find it necessary?
S3 · E29
14 lug 2018
34:09
Stagione 2
27: Peer Pressure (Cellular Automata)
The fabric of the natural world is an issue of no small contention: philosophers and truth-seekers universally debate about and study the nature of reality, and exist as long as there are observers in that reality. One topic that has grown from a curiosity to a branch of mathematics within the last century is the topic of cellular automata. Cellular automata are named as such for the simple reason that they involve discrete cells (which hold a (usually finite and countable) range of values) and the cells, over some field we designate as "time", propagate to simple automatic rules. So what can cellular automata do? What have we learned from them? And how could they be involved in the future of the way we view the world?
S2 · E27
14 mag 2018
51:48
25: Pandemic Panic (Epidemiology)
The spectre of disease causes untold mayhem, anguish, and desolation. The extent to which this spectre has yielded its power, however, has been massively curtailed in the past century. To understand how this has been accomplished, we must understand the science and mathematics of epidemiology. Epidemiology is the field of study related to how disease unfolds in a population. So how has epidemiology improved our lives? What have we learned from it? And what can we do to learn more from it?
S2 · E25
13 apr 2018
44:34
Why Uncertainty Is Science's Greatest Strength with Stuart Firestein
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. Chapters 03:00 Predictability and the sea of uncertainties 04:08 Science as a search for probabilities and multiple solutions 06:16 Biological classification and the dynamic nature of species 09:10 The optimistic view of a branching universe 12:41 Probability as the language of optimism 16:48 Two types of probability and their roles 17:50 AI, probabilistic models, and the future of certainty 21:40 Science and the creation of better ignorance 23:21 The importance of asking questions over giving answers 27:21 Authority versus knowledge in science 30:04 Pluralism and multiple solutions in science 32:46 Science in the gray area of uncertainty 35:39 The brain and randomness in thought 39:44 Science as a source of hope and optimism Follow Breaking Math on Substack (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 on Instagram (https://www.instagram.com/profnoahgian/) X (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on X (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: breakingmathpodcast@gmail.com
6 ago 2026
43:04
Robot Proof: Why Better AI Starts With Better People with Vivienne Ming
Neuroscientist, entrepreneur, and author Dr. Vivienne Ming joins Autumn and Noah to make the case that if we want better AI, we need to build better people first. We get into why AI tutors that hand students answers make learning worse, not better; what her research on "hybrid intelligence" reveals about the human traits — not the AI model — that predict elite human-AI collaboration; a wild experiment running Dungeons & Dragons with Claude and Gemini as dungeon masters to expose the gap between knowing and understanding; her case for "fiduciary AI," legal duty-of-care standards for tutors, hiring tools, and diagnostic models; and the real story of a hiring algorithm that learned to discriminate against women after every explicit gender marker was stripped out. Chapters 02:20 Why build this book now? The importance of human qualities 04:16 AI in education and the concept of robot-proofing 06:37 The median student and AI personalization 09:31 The limitations of AI understanding and theory of mind 11:30 Building better people with AI and human interaction 14:23 Hybrid intelligence and the role of human-AI collaboration 23:56 Case study: AI in Dungeons & Dragons 30:42 AI's strengths and limitations in understanding and cognition 37:34 The science of purpose and its impact on life and society 44:44 The collective intelligence of humans versus AI 46:54 Key takeaway: Build better people for better Follow Vivienne Ming on X (https://x.com/neuraltheory) Get Vivienne's book, Robot Proof: (https://amzn.to/3Tz21aP) Follow Breaking Math on Substack (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 on Instagram (https://www.instagram.com/profnoahgian/) X (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on X (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: breakingmathpodcast@gmail.com
25 lug 2026
59:25
Why Nothing Works: Robber Barons, Algorithms & Governing AI
In this episode, Historian and author Marc Dunkelman to explain why the 19th-century fight over railroad power is the exact fight we're about to have over algorithms and AI. Drawing on his acclaimed book Why Nothing Works: Who Killed Progress — and How to Bring It Back (a Best Book of the Year in the Financial Times and The Economist), Marc unpacks the two competing tools America has always used against concentrated power — antitrust vs. regulation — and why our government's "endemic diffusion of authority" now means nobody can decide anything, from congestion pricing to clean-energy transmission lines to AI safety. CHAPTERS 04:52 — When private projects come back to the public: Warp Speed, DARPA, CHIPS 08:55 — Two ways to fight concentrated power: break them up vs. regulate 10:52 — Railroads, island communities & the birth of regulation 12:29 — The railroad = algorithm parallel 20:33 — Why nothing gets built: the diffusion of authority 27:30 — "A voice without a veto" and the AI moment 32:53 — Where should government draw the line on new tech? 37:20 — Dunkelman the pragmatist: there is no simple answer 38:21 — Where math and AI can genuinely help public policy 40:46 — The lesson we keep overlooking Follow Marc on X [https://x.com/MarcDunkelman] Get Marc's book, Why Nothing Works: https://amzn.to/4pbFvAB] Substack (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 on Instagram (https://www.instagram.com/profnoahgian/) X (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on X (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: breakingmathpodcast@gmail.com
10 lug 2026
44:02
Can Math Save Journalism?: Julia Angwin on Proof, Power, and Amazon's Algorithm
In this conversation we chat with Julia Angwin — Pulitzer Prize-winning journalist, founder of Proof News, and former Wall Street Journal and ProPublica reporter — to make the case that journalism should function more like mathematical proof than anecdote. We cover how Angwin's team at The Markup used a decision-tree model to prove Amazon was favoring its own products in search results by an 8-to-1 margin — a finding the House Antitrust Committee later cited when referring Amazon to the DOJ for possible perjury. We dig into her "ingredients label" approach to reporting at Proof News (hypothesis, sample size, techniques, limitations), the difference between mathematical proof and the scientific method, and why she thinks control over algorithmic media is now the central battleground for authoritarian power. She also unpacks her new book on resisting authoritarianism, built from interviews with dissidents worldwide, including the "Swiss cheese" model of personal security and why perfectionism is dangerous in a crisis. Chapters 09:50 Proof News: A New Era in Journalism 19:56 Data-Driven Investigations: A Case Study 30:02 The Future of Journalism and AI 32:53 The Evolution of Search Rankings 35:06 The Role of Algorithms in Information Access 36:41 Fighting Authoritarianism Through Journalism 44:52 Community Resistance Against Authoritarianism 48:33 The Dangers of Perfectionism in Resistance 51:26 Declaring a Position in Journalism 56:25 The Importance of Math in Modern Society Julia Angwin's book, “On Courage” (https://amzn.to/448G8kY) Follow Julia Angwin on X (https://x.com/JuliaAngwin/) Bluesky (https://bsky.app/profile/juliaangwin.com) Proof News (https://www.proofnews.org/) Follow Breaking Math on Substack (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 on Instagram (https://www.instagram.com/profnoahgian/) X (https://x.com/ProfNoahGian) Follow Autumn on X (https://x.com/1autumn_leaf) Instagram (https://www.instagram.com/1autumnleaf/) email: breakingmathpodcast@gmail.com
2 lug 2026
52:49
The Proof in the Code: How Lean Is Quietly Rewriting Trust in Math (w/ Kevin Hartnett)
In this episode, Autumn and Noah talk with Kevin Hartnett about why mathematicians are willing to spend years reducing an idea to a level of detail a machine can check, whether formal verification can catch an AI that's technically correct but fundamentally misaligned, the cold-start problem that kept earlier theorem-provers niche, and what it means for the future of mathematical trust once AI can generate proofs faster than any human community can read them. Timeline: 00:00 Introduction to Lean and Its Significance 03:18 The Journey of Writing the Book 05:13 Human Element in Mathematical Formalization 06:57 Understanding Formal Proofs in Mathematics 11:21 The Origins of Lean and Its Purpose 13:03 Misalignment in Software Specifications 14:39 Building Mathematical Libraries in Lean 17:23 Ensuring Accuracy in Mathematical Foundations 22:00 Overcoming the Cold Start Problem in Lean Adoption 24:36 The Future of Mathematical Proofs 30:26 AI's Role in Mathematics 38:29 Expanding Beyond Mathematics 41:40 The Long-Term Impact of Lean The Proof in the Code is out now from Quanta Books. (https://amzn.to/3SuNlJm) Follow Kevin Hartnett on X (https://x.com/KSHartnett) Bluesky (https://bsky.app/profile/kevinhartnett.bsky.social) Follow Breaking Math on Substack (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 on Instagram (https://www.instagram.com/profnoahgian/) X (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on X (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: breakingmathpodcast@gmail.com
24 giu 2026
45:38
1 di 20