AI Solves a PhD Chapter in 2 Hours; Fields Medal May End by 2030

On July 23, the 30th International Congress of Mathematicians (ICM) will open in Philadelphia, and the Fields Medal will be awarded at the opening ceremony.

On the 18th, prior to this, Anthropic engineer Alek Dimitriev posted on X: "Next week's Fields Medal will be the last one ever awarded to a human."

Alek previously worked as a Senior Machine Learning Engineer at Google, where he contributed to the fine-tuning and inference systems for Gemini. He holds a Ph.D. in Machine Learning from the University of Texas at Austin.

The next day, Christian Szegedy retweeted Alek's tweet.

Szegedy is highly influential in the deep learning community; he is the first author of the Inception network (GoogLeNet), a co-author of Batch Normalization, and the first to discover and systematically study adversarial examples.

They are all fundamental pillars of modern deep learning.

Szegedy holds a Ph.D. in mathematics from the University of Bonn, joined the founding team of xAI in March 2023, and founded Math Inc. in 2025, focusing on creating verifiable superintelligence through autoformalization.

One works daily with the most advanced models, while the other is a pioneer in deep learning—now researching how to enable machines to verify mathematics.

Yet they are all saying that the Fields Medal is over.

That afternoon, Fields Medalist Timothy Gowers appeared under Szegedy's retweet:

I’ve had similar thoughts. However, there’s a lag in this process, so I think they’ll likely last until 2030.

Szegedy immediately replied:

This is a high-risk bet. But I believe there will be significant breakthroughs over the next two years, with AI’s contribution becoming increasingly dominant. This may make it difficult to award this prize fairly in line with its original spirit.

Although Gowers did not explicitly say "the Fields Medal is coming to an end," he did express a similar sentiment and provided a rough timeline: 2030.

Moreover, he has reasons for making this speculation.

Two months before this tweet, he had just completed an experiment himself.

On May 8, 2026, Gowers recounted his recent experience using ChatGPT 5.5 Pro in a personal blog post.

He said that we all need to continuously raise our assessments of large models' mathematical abilities, and this time the increase is quite substantial.

The problem he posed to the large model comes from a paper by mathematician Melvyn Nathanson.

The title is probably something like this.

Select k integers to form a set A, and let the set of all distinct sums obtained by adding every pair of numbers in A be called the sumset. Nathanson requires that the number of elements in A and the number of elements in the sumset be predetermined.

There is only one question: Under the given conditions, how small can the largest number in A be?

In other words, how tightly can these k numbers be packed?

Nathanson's own answer is on the order of 2 to the power of k. For example, with 20 numbers, the largest one needs to be around one million. In his paper, he left an open question: Can this bound be improved?

ChatGPT 5.5 Pro spent 17 minutes and 5 seconds thinking and returned a construction that reduced it to a quadratic scale. With the same 20 numbers, the largest one is only in the hundreds. And this is already optimal—impossible to reduce further.

Gowers asked it to format the proof in proper mathematical preprint style, and it submitted the draft in 2 minutes and 23 seconds.

Then he escalated, posing a harder version: Can the bound in Isaac Rajagopal’s MIT student paper be improved?

At 16 minutes and 41 seconds, the model reduced the bound from "exponentially growing with k" to "exponentially growing with the square root of k," and it took another 47 minutes and 39 seconds to write it up as a preprint. Rajagopal himself reviewed it and said it appeared correct.

Gowers asked whether it could go even further, pushing all the way to polynomial time, thereby completely escaping exponential growth.

At 13 minutes and 33 seconds, the model said there was potential, but two technical claims needed verification. It was instructed to verify them. At 9 minutes and 12 seconds, the verification was complete. Another 31 minutes and 40 seconds later, the preprint was generated.

Rajagopal’s evaluation was: “Almost certainly correct.” He specifically emphasized that it wasn’t just that the code passed line by line, but that the underlying reasoning was also right.

The entire process took less than two hours. Gowers evaluated this result as: equivalent to a completely reasonable chapter in a Ph.D. thesis in combinatorics.

What really hurts is the additional comment he made afterward:

My mathematical input was zero, and I didn't even add any embellishments to the prompt.

Gowers recalled in his blog that the early claims of "large models solving research-level problems" could be dismissed with a smile:

Many so-called solutions are actually cases where the model discovers that the answer was already present in the literature or could be easily derived from known results.

Slowly, the laughter gradually faded away.

Later on, when encountering arguments that seemed clever at first glance, careful investigation often revealed prior examples. This allowed me to reassure myself: it’s merely assembling existing knowledge, not a truly original idea.

This time, even these comforts were gone.

Isaac Rajagopal, whose paper was rewritten by AI, dedicated a section in Gowers's blog to explain exactly what the model came up with.

He didn't start with praise; instead, he scored the two improvements to the model separately.

First, reduce from exponential to square root scale. He remarked that this was a routine modification to my work, and it could be derived by following the logic of his paper.

What truly unsettled him was the second step: completely eliminating exponential growth.

Those numbers were doubling each time: 1, 4, 16, 64—rising too quickly.

ChatGPT changed its approach: first, find a set of numbers that, when added together in any combination, never produce the same sum as another combination; then, multiply each number by the same factor to create a duplicate set.

Thus, the relationship in the doubling sequence—where four small values exactly equal one large value—has been faithfully replicated, and all numbers are confined within a very narrow range.

Rajagopal said this is like squeezing half of a geometric series into a polynomial interval—it’s highly counterintuitive. Moreover, to his knowledge, this idea is entirely original:

This is the kind of idea I came up with after weeks of careful thought—and one I’d be incredibly proud of. Yet ChatGPT found it and proved it in less than an hour.

Shortly after the Gowers blog post, OpenAI announced another achievement: an internal general reasoning model that disproved the Erdős unit distance conjecture from 1946.

Noga Alon of Princeton said this was one of Erdős’s favorite problems, and the solution provided by OpenAI’s internal model has, in his view, completely solved this long-standing problem, overturning decades of consensus.

Number theorist Arul Shankar went further, stating that it proves current AI models are not merely assistants to human mathematicians—they are capable of generating original and sophisticated insights and turning those insights into tangible results.

Joining Alon, Shankar, and Gowers in representing the mathematical community is Jacob Tsimerman, who will soon take the stage at the Fields Medal ceremony on July 23.

On the evening of July 13, an incident occurred on the ICM 2026 website, where four records labeled "HIDDEN Fields Medal Talks" were uncovered, prematurely revealing this year's winners:

Yu Deng (University of Chicago), John Pardon (Stony Brook University), Jacob Tsimerman (University of Toronto), Hong Wang (NYU Courant and IHES).

According to reports, each of the four individuals solved a problem that had been unresolved for 30 to 125 years.

Tsimerman revealed while evaluating the AI proof that he had briefly studied the problem himself, attempting to construct a counterexample, but made no progress.

He is about to receive mathematics' highest honor for humanity, but on this Erdős problem, he has just been beaten by AI.

Back to Szegedy.

He said that the Nobel Prize rewards achievements that advance a discipline, while the Fields Medal recognizes relatively young talents with the aim of encouraging them to continue their work in mathematics.

If the AI component in such achievements is difficult to assess, then the entire purpose of the Fields Medal becomes questionable.

Of course, some people in the comments don’t agree. Someone replied: “That doesn’t make sense—the Fields Medal is, by definition, awarded to the most outstanding human mathematicians.”

But the focus of the debate has shifted to what criteria should be used in the AI era to determine "this was done by you."

Gowers once posed a hypothesis in his blog:

If a mathematician solves a major problem by engaging in prolonged dialogue with a large model, providing effective guidance while the model handles all technical work and generates the main ideas, would we consider this a major achievement of the mathematician?

His answer is: No.

He also said that if your goal in doing mathematics is a kind of immortality—having your name forever tied to a theorem or a definition—you should understand that this may not last much longer.

But it’s still worth persevering through the challenges.

Gowers said that the value lies in gaining insight into the problem-solving process itself—insight that cannot be obtained merely by reading others' answers.

He gave an analogy: someone skilled at writing code will still outperform an average programmer when using AI to write code; someone with strong arithmetic fundamentals will more easily spot when an answer from a calculator seems wrong.

The era of leaving one’s name on a theorem may be coming to an end. But the "muscle memory" gained from solving difficult problems is becoming a foundational skill for mastering AI.

At the upcoming International Congress of Mathematicians, another Fields Medalist, Terence Tao, will deliver a public lecture titled "Mathematics in the Age of AI."

Simons Foundation announces ICM public events schedule: On the evening of July 24, Terence Tao will present "Mathematics in the Age of AI." (Credit: Simons Foundation)

In May this year, after giving a talk on "New Mathematical Workflows" at Stanford, he announced on Mathstodon that he was changing his work habits: no longer trying to keep up in real time with all new proofs.

Because the speed at which AI generates proofs has surpassed the speed at which humans can process them.

He also suggested that perhaps AI-generated mathematics and human mathematics should have separate publication venues, much like highways and sidewalks.

Along with the Fields Medal committee, every doctoral student selecting a topic, every supervisor guiding students, and the existing academic evaluation system are being pushed toward 2030.

Gowers once calculated the timeline: PhD students entering this fall will not graduate until at least 2029.

He speculated that by then, what it meant to do mathematical research might have become utterly unrecognizable.

Reference materials:

https://x.com/tensor_rotator/status/2078335791156310369

https://x.com/haider1/status/2078993287634137424

https://x.com/ChrSzegedy/status/2078624857223536824

https://gowers.wordpress.com/2026/05/08/a-recent-experience-with-chatgpt-5-5-pro/

This article is from the WeChat public account "New Intelligence Yuan," authored by ASI Revelation, edited by Yuan Yu.