Modern mathematics has never been solely the product of solitary individuals. Every theorem rests upon a long history of concepts, notations, methods, counterexamples, and intergenerational exchanges.

Nevertheless, to this day, we often discern a central mind behind each major work. We might speak of one person's perspective, another's intuition, a technique bearing the hallmark of a specific school of thought, or an idea born of the author's unique intellectual history.

The personal imprint on mathematics is real. We view the 2026 Fields medalists, announced on July 23, Yu Deng, John Pardon, Jacob Tsimerman, and Hong Wang as four central minds who forged four distinct journeys of discovery, each stamped with their own personal signature, don't we?

Will this perception remain unchanged in future?

In May, an internal OpenAI model produced a new family of configurations that refuted a decades-old belief regarding the planar unit distance problem originally posed by Paul Erdős in 1946. The problem asks for the maximum number of pairs of points that can be placed at exactly one unit distance apart on a flat plane.

While the result did not fully solve the problem, it disproved the hypothesis that square-grid-based configurations were essentially near-optimal.

The proof was subsequently verified by a group of mathematicians. Among the experts who publicly praised the novelty of the argument was Tsimerman, the 2026 Fields winner.

A person holds a Fields medal. Photo by AFP

I myself have recently had the opportunity to observe, at close quarters, the shift from using machines merely as tools to using them as partners in discovery.

As someone passionate about both mathematics and AI development, the moment the problems for the 67th International Mathematical Olympiad held in Shanghai from July 10 to 21 were released, I tasked ChatGPT 5.6 with attempting to solve them.

I used a workflow similar to the one I employ in my daily professional life though my actual job does not involve solving math problems.

Surprisingly, ChatGPT fully solved all six exam problems in two days, a feat equivalent to a perfect gold medal, an achievement reached by only seven contestants in the competition. I went on to develop this method into a procedure for tackling an open problem known as the Lonely Runner Conjecture (LRC), which has remained unsolved since 1967.

After two days of intensive work, the results were substantial enough to form the basis of a serious research paper for a specialized journal, even though the final solution was not yet complete.

I do not view these systems as mathematicians, nor do I regard the problems I have tackled as personal achievements.

But what is noteworthy is the shift in the working structure. A single question branches out into multiple paths. Each branch involves a process of gathering literature, constructing arguments, hunting for counterexamples, or playing the role of a critic.

Intermediate results feed back into the process, transforming the original question. Humans no longer simply issue commands and wait for answers; instead, they must design an environment where various possibilities can be generated, clash with one another, be discarded, and be verified.

There are times when the AI places too much faith in an appealing result, forcing me to steer it back to the original constraints.

At other times, I might be on the verge of abandoning a line of inquiry sensing it holds no promise only for a different branch of reasoning to uncover a structure worth preserving.

Most outputs still require rigorous verification. What fascinates me is not a perfect success rate, but the way the two parties continuously reshape each other's conceptual landscape.

It is no longer a simple relationship between a user and a passive tool, yet it does not quite mirror a collaboration between two mathematicians either; it is a form of partnership that still lacks a name.

These experiences suggest a possibility: the creators of future mathematics may not be solitary individuals, but rather a multi-layered collaborative system.

Humans provide direction, select problems, interpret significance, establish verification standards, and bear ultimate responsibility.

Meanwhile, AI expands the search space, maintains multiple lines of reasoning, uncovers distant connections, and traverses paths that would be difficult for a single person to cover alone.

In this context, contributions cannot easily be quantified as percentages, because the idea that triggers a chain of machine reasoning is itself transformed by the resulting output, which in turn alters the human's initial intuition.

Therefore, I am not suggesting that a machine will walk onto the stage or that a model’s name will be engraved on a Fields Medal in the near future. What is worth considering is that the honored work might no longer originate within a single brain, nor can it be fully recounted through the intellectual biography of one individual.

This reality will compel the field of mathematics to establish new standards regarding publication, contribution, and accountability.

Research papers must more accurately describe the stages where AI played a role—ranging from literature searches, hypothesis generation, and the proposal of lemmas to formal verification.

The community needs to distinguish between using AI merely as a search tool and a system generating a conceptual breakthrough.

Award committees can no longer simply ask who signed the manuscript; they must understand how the discovery process itself was organized.

A sound standard should neither pretend that AI does not exist nor grant authorship to machines in a way that obscures human responsibility.

The redistribution of roles rarely waits for a consensus to emerge before it begins; it often stems from small moments—an unexpected line of proof, a machine-generated hypothesis, or a structure that reveals itself only when humans and AI engage in a sufficiently deep critical dialogue.

At first, we call it assistance. Then, collaboration. Eventually, we realize there is no longer a way to separate the two parties without compromising the achievement itself. The boundary does not vanish overnight; it fades with each successive project until the old language no longer suffices to describe the new reality.

The recently awarded Fields Medals may well be the last for which we can be relatively certain the story behind them belongs to a singular protagonist.

I feel a touch of nostalgia at this thought, yet I feel even more fortunate—lucky enough to have been born late enough to witness the closing chapter of a magnificent form of creativity, and early enough to step into the era that follows.

*Nguyen Canh Lam is an AI, real-time robotics researcher and developer.