Christian Szegedy has spent his career at the point where mathematics and machine learning meet. He helped build GoogLeNet and wrote the paper that named adversarial examples, and in 2023 he was among the founding members of Elon Musk’s xAI. When a person with that record writes a long essay on where mathematics is going, the field tends to read it. The essay he posted this week argues something more provocative than most: that the two-thousand-year tradition of the lone genius climbing a mountain alone is finished, and that mathematics is about to become an industrial process.
The title asks the question directly: “Where Is Mathematics Going?” Szegedy’s answer is that it is going the way of mapmaking. For centuries, the story of mathematics was told through solitary figures. Now, he writes, the field is shifting from the image of a genius scaling a cliff by hand to that of an aircraft surveying a whole continent, with machines doing in hours what once took a human lifetime.
The evidence he assembles is recent and specific. In early September, Anthropic’s internal model spent eleven days writing a complete proof of Fermat’s Last Theorem in the proof assistant Lean. Days later, OpenAI said a system running ten thousand agents for eighty-eight hours had conquered the Navier-Stokes equations, a Millennium Prize problem that has resisted solution since the nineteenth century. By late September, OpenAI reported that its model had solved more than a hundred long-standing open problems. The Jacobian conjecture, another problem that has stumped professionals for decades, appears on the list of the fallen.
None of this is uncontested, and Szegedy does not pretend otherwise. Stephen Wolfram has pushed back, asking what it means for a field when no human can check, or even follow, the proofs being produced. Kevin Buzzard, the mathematician who has spent years trying to formalize the discipline’s language, has described the profession’s mood as a kind of grieving, a process he mapped onto the five stages of loss. The community is not celebrating so much as trying to figure out whether it still has a job that requires a human.
Szegedy’s own view is that this grief is natural but misdirected. His argument, developed across a decade of work on what he calls autoformalization, is that mathematics was never really about the heroism. It was about turning natural-language argument into something verifiable. The machines are simply doing that translation at a scale no human can match. What is dying, in his telling, is not mathematics but a particular romance about how it is done.
The timing of the essay is not accidental. Szegedy left xAI in early 2025 and went on to found a company, Math Inc., built around the idea of verified superintelligence through autoformalization. His startup’s agent, Gauss, had earlier completed the formalization of a theorem that had stalled for eighteen months under human effort. A person building a business on machine-checked mathematics has an obvious stake in declaring the heroic era over, and critics have noted that the essay reads as both a prediction and a pitch.
Yet the underlying trend is hard to dismiss. Formal proof assistants, once a backwater used by a handful of specialists, are now the medium through which frontier models are demonstrating their results. Journals and funding agencies are quietly debating what to do with a flood of machine-generated proofs. The question is less whether AI can do mathematics than whether the field can absorb the output, and whether the humans trained to produce a few theorems a year will find a role verifying, directing, and interpreting what the machines turn out by the thousands.
The biography gives the argument its weight. Szegedy was first author on “Going Deeper with Convolutions,” the 2015 paper that introduced the GoogLeNet Inception architecture, and co-author on the paper that named adversarial examples and on Batch Normalization, which won the 2025 Test-of-Time award at ICML. He is not an outsider to the discipline declaring its death; he is someone who helped build the machines now doing the proving. That background is why his essay, however much it doubles as marketing for Math Inc., has been read as a serious forecast rather than a provocation.
Szegedy’s closing point is the one that has traveled furthest. Mathematics, he writes, will not disappear. It will become infrastructure: formalized, verifiable, and industrialized, a service rather than a calling. The image of the solitary climber will survive as history, the way the age of the surveyor survived the arrival of the airplane. What will not survive, he argues, is the assumption that the only path to a proof runs through a single human mind working alone.
