The Progress of AI Concerns Leading Mathematicians

Terence Tao, a professor at UCLA and winner of the Fields Medal in 2006, published a warning on the Mathstodon network on September 8, 2026, which has circulated widely in academic circles. According to him, AI is no longer just assisting researchers; it threatens the very essence of human understanding and fundamental research. This is because artificial intelligence is drying up the pool of "good open problems." These unresolved questions are what truly advance a scientific field.

In Brief

• AI solves millennia-old problems in a matter of days, compared to years for humans.
• Terence Tao warns: AI is exhausting the "good questions" in mathematics.
• Mathematicians fear a devaluation of their role and discoveries.
• The community calls for new rules for the use of AI in research.

AI Solves Millennia-Old Problems in Record Time

Since May 2026, announcements related to artificial intelligence have been coming in at a frantic pace. OpenAI first invalidated Erdős's conjecture on unit distances, a problem that has been open since 1946. A few weeks later, the same AI company claimed to have solved one of the seven "Millennium Problems" from the Clay Mathematics Institute: the existence and regularity of solutions to the Navier-Stokes equations. These equations describe the movement of fluids.

According to Tristan Buckmaster, a mathematician behind a promising approach, OpenAI's AI completed in one weekend what he and his colleague Levent Alpöge (an employee of Anthropic) had been trying to finalize for months.

That's not all! In August 2026, OpenAI also published ten new major mathematical and computational results obtained with its Astra model. These cover:

• geometry;
• cryptography;
• coding theory.

For its part, Anthropic used Claude to formalize the proof of Fermat's Last Theorem in just 11 days. This AI company has just announced an imminent IPO.

Terence Tao: AI is Exhausting the "Good Questions" in Mathematics

In a post published on Mathstodon, Terence Tao, regarded as the greatest living mathematician, issues a clear warning. According to him, the real danger is not that AI solves problems, but that it does so too quickly before the community has had time to learn from them.

He wrote:

The indiscriminate use of powerful solution-extraction tools may achieve the immediate goal of solving problems, but at the cost of sustaining the ecosystem for the next wave of progress.

For Tao, the value of a mathematical problem lies as much in its solution as in the journey taken to arrive at it. Indeed, this process allows for:

• discovering new methods
• finding new connections between fields
• (sometimes) reformulating the question itself.

However, with AI, this journey is short-circuited. In this sense, Tao warns:

We have now seen that even the rumor that someone is working on a problem can trigger a massive amount of AI-fueled effort to flatten it before the original research project has time to reach its full potential.

Decoding: AI transforms mathematics from a discipline of "scarcity of proofs" into a discipline of "abundance of proofs." This threatens to devalue human work.

Mathematicians Facing an Identity Crisis with AI?

Beyond Tao's statements, the entire profession is questioning itself. "If the main goal of mathematics is to prove theorems, it becomes easy to ask: now that machines seem to be able to do it almost at will, what use are we?" asks Henry Yuen, a mathematician at Columbia University, in an interview with The Telegraph.

In June 2026, more than 3,000 mathematicians signed the Leiden Declaration. This document calls for:

• responsible use of AI;
• rigorous verification of results;
• appropriate citation of human and artificial contributions.

For his part, Terence Tao proposes a solution: classify certain problems as requiring analysis. This means that a raw answer (notably one provided by artificial intelligence) only counts if it is accompanied by understandable and instructive reasoning.

What Future for Mathematics in the Age of AI?

Some see AI as a productivity tool. The fact is it frees humans from tedious tasks, allowing them to focus on formulating new questions. Others, however, fear an industrialization of proof. According to them, intellectual value could thus fade in favor of speed.

Nevertheless, both sides agree on one point: the rules must change. The Leiden Declaration thus emphasizes transparency and recognition of contributions. But how to apply these principles in a race where AI models are not public and proofs are generated in a matter of hours?

In any case, AI has crossed a threshold in mathematics. The ball is now in the community's court: to define new rules so that artificial intelligence remains a tool and not a replacement.