# Math vs. Machines | Radiolab Podcast

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**Score: 69/100 · skim**

Cornell mathematician Steve Strogatz tells Radiolab's Soren Wheeler that AI went from failing grade-school arithmetic in 2022 to solving problems the world's best mathematicians couldn't by 2026. That progress ended with OpenAI's claimed solution to the Navier-Stokes Millennium Problem. Strogatz isn't mainly afraid for his job. He's afraid of a future where machines act as "infallible but opaque oracles" that give correct answers nobody can understand, which would undercut the understanding that has driven math, science and, for him, a meaningful life.

- **0:00-2:18** — **Setup: why mathematicians are rattled.** Wheeler pulls Strogatz away from X (Twitter), where mathematicians were reacting to OpenAI's announcement days earlier that it had solved a major open problem. Strogatz says the field is "on a trajectory" that may turn out happy or very sad, and admits he's "terrified." Wheeler explains the fear isn't about hacks, the economy or job loss but about Strogatz's sense of purpose, which he frames as a basic human question.

- **2:18-4:45** — **From joke tool to emergent mathematician.** Strogatz started using ChatGPT in November 2022 for gags, like poems in the style of Malcolm Gladwell, then tested it on math. At first it failed elementary arithmetic and was easy to fool. Over time it handled clumsy algebra, then real reasoning problems and good International Math Olympiad scores, not just number crunching. He calls this an "emergent property": the models were trained on language, yet language seems to carry enough logic to do math, and nobody fully understands why. Visual reasoning stayed a weak spot until recently.

- **4:45-5:20** — **The timeline speeds up.** Strogatz gives the sequence: high-school level around 2024, strong college-student level in 2025, first-rate (but not world-best) mathematician by about March 2026, and by May 2026 solving problems the best humans had failed to solve. Wheeler notes how fast this was: a year earlier Strogatz was about as worried as he'd be about Wheeler taking his job.

- **5:20-7:30** — **The unit-distance problem, the first big moment.** The problem: for a given number of points on a plane (pegs on a board), what's the most pairs you can place exactly one unit apart? It's pure discrete geometry with no practical motive. For decades people assumed a simple grid-like arrangement was about the best possible, and the open question was whether to prove that or find a counterexample. In May, an OpenAI model found a better arrangement. Experts called the argument "beautiful" and "elegant" because it linked two branches of math nobody knew were connected.

- **7:30-8:23** — **Chain of thought.** The models now produce a readable "chain of thought" that lays out their reasoning in natural language. It includes reactions like "this is gonna work!" with exclamation points and swearing, which the models learned from how people write about discoveries. This matters because in the unit-distance case humans could actually follow what the machine did.

- **8:23-10:10** — **The "Fosbury flop" analogy and a summer of solved problems.** Dick Fosbury's backward high jump, which won gold and set an Olympic record in 1968, looked ridiculous but became universal once others copied it. Likewise, mathematicians borrowed the AI's unit-distance idea and applied it to other problems, the good kind of AI impact. Strogatz calls May 2026 the moment "a world-caliber mathematician that was not human" appeared. From May to September, harder and more central problems fell one after another, which he says traumatized much of the math community.

- **10:10-12:47** — **Navier-Stokes, a Millennium Problem.** In September 2026 OpenAI announced a solution to the Navier-Stokes problem, one of seven Millennium Problems set in 2000 as goals for the century. Strogatz calls them "cherished mountaintops." The 1800s equations describe how fluids move (water, air, honey, lava, blood) and are used for weather forecasting and ventilation design. The open question was whether they can produce physical nonsense. The AI reportedly found a vortex that keeps shrinking while getting stronger, like a tightening tornado, until the equations blow up to infinity at a singularity.

- **12:47-14:47** — **How it was done, what it cost, and a dispute over credit.** Early reports say about 10,000 AI agents worked partly independently and partly together for about four days, roughly 100 years of round-the-clock work. The estimated cost was $15–20 million for a problem with a $1 million prize, so the point was prestige in the OpenAI vs. Anthropic rivalry, not money. The work built on a strategy from Spanish mathematicians Diego Córdoba and his student Luis Martínez-Zoroa, who were making progress at human speed but might have needed 5–10 years or never finished because the calculations were so large. Wheeler also notes questions about whether OpenAI used the work of Tristan Buckmaster and Levent Alpöge without crediting them; Strogatz says he has no inside knowledge of that.

- **14:47-17:00** — **Why this one feels different: opaque instead of elegant.** Unlike the unit-distance result, the 160-page Navier-Stokes write-up is so complex that experts don't yet know how the AI solved it. Strogatz calls it "inhuman computation" and finds it off-putting. For him the value of the big problems is partly the struggle and the learning, and he wants to know *why*. His core worry is a future where machines are so far ahead that we can't learn from them and get only yes/no verdicts from "oracles that are infallible but opaque."

- **17:00-22:03** — **Regina Barzilay: the strongest case for opaque AI.** Barzilay, now an MIT computer scientist, was diagnosed with breast cancer at 43 in 2014. She had no symptoms, no family history, a 7-year-old son, a recent divorce, and no family support in the US. Her doctors couldn't tell her odds for cases like hers. She suspected her earlier mammograms held signs no human could see, so she collected about 250,000 mammograms with long-term outcomes and trained a machine-learning model to predict risk from a single mammogram. It's now state of the art and has been validated worldwide, but nobody, including Barzilay, knows what it's seeing, so doctors can't be told what to look for. Her answer to Strogatz: "Why would we limit the machine to what humans can understand? We have to save lives here." Strogatz finds this haunting and grants that in medicine, refusing to use it would be "morally perverse."

- **22:03-24:15** — **Why understanding has practical value.** Strogatz stresses he's an applied mathematician, so his point isn't just the pleasure of an "a-ha" moment. He cites moon missions and ultrasound design and argues that 400 years of math plus science built the modern world. Insights from struggling with one problem, even an abstract one, often pay off in other fields. His summary: "Understanding is the key to power." He says AIs can already solve almost everything mathematicians consider worth solving, and the hardest problems are "a matter of time."

- **24:15-28:24** — **Torn between two futures.** On the pessimistic side, math could become a hobby like Sudoku, played for fun with no discoveries that matter, which raises the question of whether young people who love math can still become mathematicians. Arguing against himself, he says we might enter a "golden age of understanding" where AIs are both the best mathematicians and the best teachers, like hearing Pavarotti sing. Over several conversations he kept changing his mind, but kept feeling sidelined and invoked the passive humans in *WALL-E*. Wheeler pushes back that most people don't understand their toasters and don't care. Strogatz agrees that's fine in everyday life but says understanding shouldn't be given up lightly, because it feels close to what makes us human and to the purpose of a short life spent being curious. He still allows that AIs might stay tools we control, "brain prostheses." He closes by saying 2026 will be remembered as either an annus mirabilis (miracle year) or an annus horribilis (horrible year) for mathematics, and he doesn't yet know which.

- **28:24-31:11** — **Outro and credits.** Production credits: Wheeler and producer Maria Paz Gutiérrez reported it, Pat Walters edited it, and Diane Kelly fact-checked it. A plug for Strogatz's book *Big Math*, co-written with Cornell colleague Alex Townsend and out November 10. A pointer to the earlier episode "The Middle of Everything Everywhere," then staff and funder credits. No new content.

**Practical takeaways:**
- **AI's math ability grew in stages, fast:** from failing arithmetic (2022) to research-level and record-breaking results (2026). Expect fields that think they're safe to see similarly sudden jumps.
- **Judge AI results by whether people can follow them, not just whether they're correct.** The unit-distance result was celebrated because humans could learn from it. The opaque Navier-Stokes proof was met with unease.
- **Opaque AI is easier to justify when lives are at stake.** Barzilay's mammogram model shows a black box can be the right call in medicine, while in research the loss of understanding may cost future insights.
- **Read headline AI claims critically.** Note the cost ($15–20M for a $1M prize), the competitive motives, and the open questions about uncredited human work behind the Navier-Stokes result.
- **Use AI output to build your own understanding** (the "Fosbury flop" pattern) rather than just taking its answers, if you want to keep the long-term benefits of knowing *why*.

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