Breaking Math is a deep-dive science, technology, engineering, AI, and mathematics podcast that explores the world through the lens of logic, patterns, and critical thinking. Hosted by Autumn Phaneuf, an expert in industrial engineering, operations research, and applied mathematics, and Noah Giansiracusa, a mathematician and leading voice in algorithmic literacy and technology ethics, the show is dedicated to uncovering the mathematical structures behind science, technology, and the systems shaping our future.
What began as a conversation about math as a pure and elegant discipline has evolved into a platform for bold, interdisciplinary dialogue. Each episode of Breaking Math takes listeners on an intellectual journey—into the strange beauty of chaos theory, the ethical dilemmas of AI and algorithms, the hidden math of biology and evolution, or the physics governing black holes and the cosmos. Along the way, Autumn and Noah speak with working scientists, researchers, and thinkers across fields: computer scientists, physicists, chemists, engineers, economists, philosophers, and more.
But this isn’t just a podcast about equations. It’s a show about how mathematics shapes the way we think, decide, build, and understand the world. Breaking Math pushes back against the idea that STEM belongs behind a paywall or an academic podium. It’s for the curious, the critical, and the creative—for anyone who believes that ideas should be rigorous, accessible, and infused with wonder.
If you’ve ever wondered:
What’s the math behind machine learning and modern algorithms?
How do we quantify uncertainty in climate and economic models?
Can intelligence or consciousness be meaningfully described in AI?
Why does beauty matter in an equation?
You’re in the right place.
At its heart, Breaking Math is about building bridges—between disciplines, between experts and the public, and between abstract mathematics and the messy, magnificent reality we live in. With humor, clarity, and deep respect for complexity, Autumn and Noah invite you to rethink what math can be—and how it can help us shape a better future.
Superforecasting Explained: How Prediction Markets Beat Experts
Wednesday, September 9, 2026 • Duration 43:13
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 Topics
The definition of forecasting and its importance
Techniques for starting in forecasting \
The role of AI and large language models in forecasting
How to interpret probabilities and conditional forecasts
Forecasting in complex systems like climate and geopolitics
Ethical boundaries and red lines in prediction markets
The impact of AI bots on forecasting accuracy and decision making
Chapters
03:06 Getting Started with Forecasting: Tools and Techniques
06:15 Beginning Forecasting as a Beginner
07:31 Gut Feelings vs Market Wisdom
08:33 The Delphi Loop and Group Forecasting
09:39 Measuring Forecast Accuracy and Skill
11:17 Forecasting Long-Term and Uncertain Events
12:40 Extrapolating Trends and Model Limitations
14:19 AI Bots in Forecasting and Their Performance
18:16 Prediction Markets as Collective Wisdom
19:19 The Future of Prediction Markets and Society
24:06 The Meaning of Probabilities and Risk Assessment
27:20 Dealing with Chaos and Unpredictability
32:52 Combining Models and Expert Opinions
36:31 Forecasting and Expertise in Science and Policy
What Actually Makes Something Alive? with Melanie Challenger
Wednesday, August 19, 2026 • Duration 48:46
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.
Chapters
08:12 The concept of purpose in living beings
09:14 The scientific view of purpose and agency
11:52 The importance of purpose and meaning in life
13:19 The danger of ignoring organism agency in science
14:34 Living beings as purposeful agents
15:35 Comparing purpose in a Roomba and a single-celled organism
18:03 Autopoetic vs allopoetic systems
20:03 Free will, agency, and the universe
23:24 The physical basis of life and energy
28:38 Aristotle's concept of psyche and purpose
33:46 The importance of understanding what life truly is
37:56 Material integration and the difference between machines and living beings
38:15 The concept of self and embodiment in life
41:09 The whole body as the agent, not just the brain
Follow 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 on
Why Uncertainty Is Science's Greatest Strength with Stuart Firestein
Thursday, August 6, 2026 • Duration 43:04
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
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Robot Proof: Why Better AI Starts With Better People with Vivienne Ming
Saturday, July 25, 2026 • Duration 59:25
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
Why Nothing Works: Robber Barons, Algorithms & Governing AI
Friday, July 10, 2026 • Duration 44:02
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
Can Math Save Journalism?: Julia Angwin on Proof, Power, and Amazon's Algorithm
Thursday, July 2, 2026 • Duration 52:49
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
The Proof in the Code: How Lean Is Quietly Rewriting Trust in Math (w/ Kevin Hartnett)
Wednesday, June 24, 2026 • Duration 45:38
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
How Data Science Exposes Injustice: Chad Topaz on Unlocking Justice
Wednesday, June 10, 2026 • Duration 40:06
What happens when the evidence of injustice is buried in messy, redacted, or inaccessible data? Mathematician and data scientist Chad Topaz joins Breaking Math to discuss his book Unlocking Justice. Together, we explore policing, sentencing, public records, Rikers Island, algorithmic risk, and the limits of quantifying human lives. This is a conversation about math, power, transparency, and the small acts of hope that can change systems.
Chapters
00:00 Introduction and Context of the Conversation
01:11 Chad's Journey from Mathematics to Social Justice
03:50 The Personal Nature of Chad's Book
04:40 Challenges in Data Collection and Access
08:03 The Impact of Data on Policing and Surveillance
09:51 Humorous Yet Tragic Data Collection Experiences
12:55 The Importance of Data Preparation and Cleaning
14:40 Navigating Imperfect Data and Its Consequences
17:48 The Balance Between Quantification and Human Stories
22:25 Incarceration and Public Health: The Rikers Island Case Study
31:36 Mathematics and Social Justice: Secrets of the Elite
39:03 Hope and Action: A Personal Journey in Data for Justice
This conversation explores the profound impact of AI and automation on the future of work, economy, and society. Featuring Martin Ford, author of 'Rise of the Robots,' the discussion covers technological progress, economic implications, policy ideas like universal basic income, and the evolving nature of jobs in an AI-driven world.
Key Topics
Impact of AI on employment and economy
Potential of universal basic income as a solution
Differences between past technological revolutions and AI
The evolution from physical robots to AI software agents
Jobs most vulnerable to automation and AI
Chapters
04:14 The Impact of Technological Revolutions on Employment
10:40 The Shift from Physical to Intellectual Automation
12:16 The Debate: Replacement vs. Augmentation of Jobs
18:01 Economic Implications of Job Displacement
21:00 Exploring Solutions: Universal Basic Income and Beyond
24:08 The Awakening of Economists
25:12 Historical Perspectives on Automation
28:27 Navigating the Future Job Market
32:57 The Role of Skilled Trades in an AI World
38:13 The Alien Thought Experiment
42:17 The Future of AI and Its Implications
44:14 The Rise of Automation and Its Impact
45:14 AI as a Digital Workforce
45:38 The Shifting Landscape of Work
46:08 Questioning the Future of Automation and AI
The Echoing Universe: How Radio Waves, AI, and Math Could Help Us Find Aliens with Emma Chapman
Friday, May 29, 2026 • Duration 47:03
Dr. Emma Chapman explains radio astronomy using the fruit bowl metaphor, explores the emotional and scientific aspects of space exploration, and discusses future technologies like the Square Kilometre Array and lunar radio telescopes. The conversation highlights the poetic beauty of the universe, the importance of connection, and the role of math and AI in understanding the cosmos with her book the Echoing Universe.
Chapters
03:17 Understanding Radio Astronomy
08:12 The Intimacy of the Solar System
09:10 Tidal Locking and the Moon
13:36 The Emotional Lives of Astronauts' Families
17:53 The Shared Experience of Space Exploration
21:58 The Emotional Resonance of Celestial Events
26:41 Facing the Universe: Overcoming Fear through Cosmology
28:16 Cultural Perspectives: How Civilizations Understand the Cosmos
30:52 Astronomy's Historical Impact: Control and Awe in Civilizations
31:05 The Unlikely Scientist: James Stanley Hay's Discovery
40:31 AI in Astronomy: Harnessing Data for Discovery
45:14 The Next Frontier: Radio Telescopes on the Moon
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