Math Vs Machine

Host Soren Wheeler brings mathematician Steve Strogatz into the conversation after OpenAI’s announcement that it had solved a major mathematical problem. Strogatz had been watching mathematicians react online and described the mood as close to an existential crisis. Wheeler initially assumes the fear might involve hacking, an economic crash, computers taking over, or mathematicians losing their jobs, but Strogatz says the deeper issue is his sense of purpose: what happens when machines can do the intellectual work that gives people meaning. They trace the story to November 2022, when ChatGPT became publicly known. Strogatz used it first for jokes, such as asking it to write poems in the style of Malcolm Gladwell, and then tested its mathematical ability. At first it could not reliably perform elementary arithmetic and was easy to fool. Over time, it progressed from clumsy algebra to solving reasoning-heavy problems and earning strong results on the International Math Olympiad. Strogatz says this ability was an emergent property: although the systems were trained for language rather than mathematics, the logic embedded in books and online writing gave them enough structure to reason mathematically.

Strogatz says the progress accelerated dramatically. In his chronology, AI reached high-school-mathematics ability around 2024, the level of a very strong college student in 2025, and the level of a first-rate—but not yet world-leading—mathematician in spring 2026. By May 2026, an OpenAI model was solving problems that the world’s best mathematicians had not solved. The first example to attract broad attention was the unit distance problem. Given pegs on a flat board, the problem asks for the greatest possible number of pairs exactly one unit apart. Mathematicians had long suspected that a simple grid was optimal, but nobody had proved the conjecture or found a better arrangement. OpenAI instead produced a counterexample: a more effective arrangement. Strogatz says experts found the argument creative, beautiful, and elegant because it connected two branches of mathematics that had not previously seemed related. Human mathematicians could then borrow and adapt the machine’s idea, much as high jumpers adopted Dick Fosbury’s backward “Fosbury flop” after he demonstrated it in 1968. The model’s chain-of-thought output also made the process appear more exploratory: it tried approaches, announced when something looked promising, and sometimes used exclamations or profanity. Strogatz stresses that the meaningful achievement was not the theatrical language but the genuinely new mathematical strategy.

On September 26, 2026, OpenAI announced that it had solved the Navier–Stokes problem, one of the seven Millennium Problems established in 2000 as especially important mathematical goals for the twenty-first century. The Navier–Stokes equations, developed by scientists Claude-Louis Navier and George Gabriel Stokes in the nineteenth century, describe fluid motion. They are used in areas such as weather forecasting and ventilation, but mathematicians have also asked whether the equations can produce fundamentally nonsensical behavior. According to the account discussed on the show, OpenAI found a condition in which the equations generate infinities. Its construction involved a vortex—roughly, a tornado becoming simultaneously stronger and smaller—creating a singularity where the equations break down. The system reportedly used 10,000 semi-independent agents that tried different approaches, collaborated, and delegated calculations. OpenAI is estimated to have spent $15–20 million, despite the problem carrying a $1 million reward, because the goal was to demonstrate capability rather than make money. The agents built on work by Spanish mathematicians Diego Córdoba and his student Luis Martínez-Zoroa, who had developed a promising strategy but might have needed five or ten human years to complete it. OpenAI’s computation took about four days; counting the agents’ work amounts to roughly 100 years of working hours. Strogatz says the community’s response differs from its reaction to the unit-distance result. The earlier proof was understandable to experts, while the Navier–Stokes write-up—about 160 pages of highly complex calculations—does not yet reveal how the AI reached its conclusion. He also notes unresolved questions about whether OpenAI used work by Tristan Buckmaster and László Székelyhidi without fully acknowledging it.

Strogatz explains why an opaque solution troubles him. The seven Millennium Problems are not merely trophies; mathematicians value the long process of trying, failing, learning, and developing techniques that can later prove useful elsewhere. He worries about a future in which machines become so far ahead that humans receive only oracle-like answers—“yes” or “no”—without knowing why they are true. Wheeler asks whether understanding is still necessary if a machine can provide a correct result. Strogatz offers a medical counterexample through Regina Barzilay, an MIT computer scientist who was diagnosed with breast cancer at age 43 despite having no symptoms, known risk factors, or family history. She underwent two lumpectomies, chemotherapy, and radiation while raising her seven-year-old son as a recently divorced immigrant without nearby family support. When she asked doctors how women with her particular diagnosis tended to fare, they could not answer because the relevant combination of age, genetics, diet, imaging, and other factors had not been studied. Barzilay then gathered about a quarter-million mammograms linked to years of follow-up data and trained a machine-learning system to predict breast-cancer risk from a mammogram. The system became state of the art and worked across hospitals and countries, but neither Barzilay nor the doctors could identify what visual clues it used. Her response was, “Why would we limit the machine to what humans can understand? We have to save lives here.” Strogatz accepts that withholding an effective medical tool would be morally perverse, but says mathematics has a different culture: understanding is part of what counts as solving the problem.

Strogatz argues that understanding is not merely the pleasant feeling of an “aha.” As an applied mathematician, he cares about how mathematical ideas meet reality—for example, safely sending an astronaut to the Moon or designing an ultrasound machine for a pregnant patient. He says four centuries of mathematics combined with science have made the modern world, producing benefits for health, technology, and society. His broader point is that knowledge gained while struggling with one abstract problem can later transform another field. If AI solves every important mathematical problem but cannot explain its methods, humans may lose the process that has historically generated transferable insight. Strogatz worries that mathematics, a discipline and culture with three or four thousand years of history, could become something people do only for amusement, like Sudoku, while machines make every consequential discovery. He is not certain that this bleak outcome is inevitable. He imagines a possible “golden age of understanding” in which computers become not only the best mathematicians but also the best teachers, showing people methods they can learn. He compares their potential work to listening to Pavarotti: machines might simply perform mathematics better than anyone has before. Yet he remains conflicted because the same achievement could make human mathematicians feel sidelined and deprive younger people of a meaningful path into the subject.

Wheeler and Strogatz widen the discussion from mathematics to human purpose. Wheeler compares a future of effortless machine assistance to the humans in the film WALL-E, sitting in lounge chairs with drinks and screens, and says that being human seems to involve trying to understand the world—including, for him, trying to understand his children. He acknowledges that people already live without understanding many everyday systems, such as how a toaster works, but says they should not give up understanding lightly. Strogatz agrees that understanding feels fundamental, then admits that the conversation has reached the question of what a human life is for. He describes human beings as a temporary “blip of atoms” organized into consciousness for perhaps 80 or 100 years before becoming dust. For him, part of the answer is curiosity and learning, and he fears he would not be able to pursue those activities in the same way if AI reaches the future they are imagining. He also leaves room for a more hopeful model in which AI remains a tool or “brain prosthesis”: humans could direct it, unplug it when necessary, and remain in charge. The episode ends without resolving whether 2026 will be remembered as an “annus mirabilis” or a “horribilis” for mathematics. Strogatz says he does not yet know whether AI’s breakthroughs will become a miracle or a disaster.