Fields Medal Winner Issues Warning: AI Could Kill Mathematics
After this year's Fields Medal was awarded, a shocking incident occurred.
Jacob Tsimerman, a professor at the University of Toronto who won the award alongside Hong Wang and Yu Deng, unexpectedly announced immediately afterward that he was joining OpenAI to shift his focus to AI safety research.
His reasoning was:
Within 2 years, AI will completely surpass humans in all domains of mathematical proof.
The next day, at the ICM 2026 site in Philadelphia, Fields Medalist Terence Tao also voiced the following with deep concern:
I believe we are entering a turbulent period — a time when the foundational values and practices of mathematics are facing a crisis.
By coincidence, another Fields Medalist, Timothy Gowers, has put forward a similar judgment.
LLMs will soon surpass humans in all aspects of mathematical problem-solving, potentially even including proposing problems, constructing theories, and formulating definitions.
He warns: The way AI "kills" mathematics may be more elegant, yet more ruthless, than we imagine.
AI won't starve mathematics to death — but it will "overfeed" mathematicians
He is far from the only mathematician who fears this power of AI.
On June 2, 2026, the *Leiden Declaration* was officially released.
As of today, the number of signatories has reached 3164.
This declaration is officially endorsed by the International Mathematical Union (IMU). Vice President Ulrike Tillmann personally stated: Mathematics has been, and must always remain, a profoundly human endeavor.
Every name on the signature list is a leading luminary in the field.
Terence Tao noted that the declaration is the culmination of months of community discussions, and he wholeheartedly supports every recommendation within it.
Peter Scholze expressed with deep regret: Just as he would not want AI to educate his own children, he refrains from using AI when working through mathematical problems, and tries his best not to read AI-generated texts.
Kevin Buzzard, Jeremy Avigad, and Steven Strogatz are all top-tier authorities in mathematics.
Timothy Gowers, however, did not sign it, as his perspective has moved beyond the idea of "AI replacing mathematicians". He has chosen to confront this far colder, grander, and unavoidable ultimate question directly:
When AI-generated proofs are not only completely correct, but also tirelessly growing exponentially, will mathematics turn into a graveyard that no one ever visits?
His concern is not that AI is too skilled at solving problems and will take mathematicians' jobs away. On the contrary: Mathematics will not die from stagnation, but from excess.
Why would that happen?
Gowers devised a thought experiment.
Imagine this scenario: If AI had never come into existence, and a sudden pandemic broke out — for some reason, it claimed the lives of all mathematicians, while leaving everyone else completely unharmed.
All mathematical literature remains intact, but no one is left who knows how to interpret it anymore.
Gowers's judgment is that rebuilding a mathematical tradition from such ruins would likely take decades.
Note that in this disaster, nothing was physically destroyed — the total loss of information is zero.
But mathematics is far more than the literature printed on paper; it lives on in the minds of mathematicians around the world — where a vast body of knowledge and deep professional intuition are preserved.
Gowers calls this a "marvel of human wisdom". If the literature is a compressed archive, then the minds of these mathematicians are the password to unlock it.
Now, imagine a slightly different version of this scenario.
This time, AI exists. And the AI is always on call, ready to explain any mathematical problem at any level of detail we desire. This would strip away a huge portion of the inherent joy that comes with the discipline of mathematics.
And with AI present, people will no longer have the motivation to spend years of arduous training to reach the standard of a typical research mathematician today.
Ten or twenty years from now, we may arrive at a point where mathematical literature is more prosperous than ever in some form, while the corresponding community of human experts quietly vanishes collectively. There will no longer be a group of people who share a common understanding of certain fields.
At that point, almost all of mathematics risks becoming a "mental graveyard" for humanity: lying dormant in papers written decades ago, but never read again.
In Gowers's view, this is a possibility that we should do everything in our power to resist.
While both scenarios end in the "death of mathematics", in the first scenario, mathematics dies from scarcity, while in the second, it dies from excess.
One is starved to death; the other is overfed to death.
Just like lakes, which can disappear not only by drying up, but also by "dying" from eutrophication.
Eutrophication refers to the process where water bodies such as lakes, rivers, and reservoirs are flooded with excessive nitrogen and phosphorus nutrients, causing explosive algal growth that turns the water surface bright green with an astonishingly high biomass. Eventually, the oxygen in the water is depleted, fish die off, and the entire lake becomes a stagnant, lifeless body of water.
ChatGPT 5.5 Pro proves a Fields Medalist wrong
Timothy Gowers's reflections on AI and mathematics are not a passing whim.
In 2022, he received funding to launch an automated theorem-proving project.
At that time, he clearly aligned himself with GOFAI (Good Old-Fashioned AI): to gain a deep understanding of how humans find proofs, and then get computers to replicate that process.
He wrote a 54-page document that explained the project's goals and methodologies in great detail.
Back then, he believed that humans excelled at distilling complexity into simplicity and finding structured proofs, while machine learning still had limitations in true understanding and transfer learning.
His goal was to generate "motivated proofs" — proofs with a transparent, interpretable process that could even be used for undergraduate teaching.
Even as late as 2025, he was publicly criticizing the training methods of existing LLMs:
Most models have only ever seen the final, polished proofs, and never the real human thought processes behind them.
He proposed building a database of "motivated proofs" to allow AI to learn genuine reasoning paths.
Then 2026 arrived.
One day in May, AI completely upended his entire worldview.
He barely provided any substantial mathematical hints at all, and simply tossed a number theory problem to ChatGPT 5.5 Pro.
The AI thought for about an hour, then output a clear, doctoral-level research result: it directly advanced the originally linear or exponential bounds all the way to quadratic, or even polynomial bounds!
After testing ChatGPT 5.5 Pro firsthand, Gowers's attitude changed completely.
He no longer just discussed "how to make AI more human-like", and began to acknowledge: LLMs are already capable of handling doctoral-level problems.
Later, when he learned that ChatGPT had solved the "unit distance problem", he was kept awake all night.
The next day, he learned that ChatGPT had only produced a counterexample, rather than a complete upper-bound proof, and he finally breathed a small sigh of relief.
Even so, he still considered this a major milestone for AI in the field of mathematics.
There is no doubt that solving the unit distance problem is a landmark achievement in AI for Math: if this paper had been written by a human and submitted to *Annals of Mathematics*, and I had been asked to evaluate it quickly, I would have unhesitatingly recommended that it be accepted.
No previous AI-generated proof had ever reached such a standard.
He felt as helpless and bitter as Lee Sedol did when facing AlphaGo: a mathematician who had spent his entire life emphasizing "understanding" was ultimately forced by the practical capabilities of machines to redefine what "research" even means.
On July 24, he simply fed his own paper to the AI for automated formalization — essentially having the AI translate the proof into machine-verifiable code.
The entire process took a week and a half, and he only spent a total of one or two hours providing prompts to complete the work.
In the end, he could not help but marvel: "The current level of technology will be more backward than any point in the future."
The elegy of mathematics
The timing of Gowers's article release is highly suggestive.
On the very same day, Peter Woit of Columbia University published a post on his blog titled "Requiem for a Field?".
Woit's comment is painfully pointed: In the past, you competed with other mathematicians, and the academic world had strong norms for attributing ideas to the person who first conceived them. But AI agents have no interest whatsoever in the "credit-naming game".
This is not exactly like chess: after chess programs surpassed humans, human chess tournaments still survived. What we are moving toward is more akin to a certain kind of program that everyone uses.
Most stars are not named after astronomers, but that does not take away from the beauty of the starry sky. If theorems no longer belong to mathematicians, it is simply the truth returning to its original state in the universe.
Gowers himself has paid a personal price.
He says he has now twice watched GPT-5.6 Pro solve in one go problems that he deeply loved and thought through carefully. On both occasions, with his consent, younger collaborators used the AI model.
The feeling was extremely strange, and far from pleasant — like having the rug abruptly pulled out from under your feet.
When machines are responsible for scientific discovery, what role do humans still have to play? In an era where the truth is expanding without limit, how can the human mind find its place?
The answer is blowing in the wind.
References:
https://gowers.wordpress.com/2026/07/26/thoughts-about-the-leiden-declaration/
https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.pdf
https://www.math.columbia.edu/~woit/wordpress/?p=15787
https://x.com/AlexKontorovich/status/2080806132298211647?s=20
This article is from the WeChat public account "