Is AI on its way to replacing mathematicians?

Kabalan Gaspard

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Is AI on its way to replacing mathematicians?<br>...and why should we care?

Kabalan Gaspard<br>Jul 14, 2026

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In 1908, famous French mathematician Henri Poincaré wrote:<br>…how vain it would be to attempt to replace the mathematician’s free initiative by a mechanical process of any kind.

If Poincaré were alive today, he wouldn’t like what he sees. This past Friday, OpenAI published a proof of a maths problem called the Cycle Double Cover conjecture - first posed over 50 years ago and unsolved until now - entirely generated by its new gpt-5.6 Sol model. This supposed breakthrough (although experts have looked at the proof and not flagged any egregious errors in it yet, it has not yet been peer-reviewed and confirmed) comes less than two months after OpenAI’s previous model made a major breakthrough in another well-known mathematical conjecture.<br>Mathematicians are now joining their peers in software engineering, consulting, finance, law, and medicine in the existential crisis of whether they will be replaced by AI. We have no shortage of “Will AI replace [X job]?” articles and blog posts, but less seems to be written about whether AI will replace an entire discipline. This article attempts to address that question, addresses why it matters, examines how good AI really is at maths today, and advances the argument that human mathematicians are still needed .<br>Who even cares?

It’s obvious why we may want to automate things like finance, taxes, plumbing, or even law and medicine. But it’s less obvious why we’d even care about replacing mathematics by a “mechanical process”. One could even ask whether we haven’t already done so, with the calculator and the modern computer.<br>In fact, the engineering behind many modern inventions we use today: secure banking and online shopping, the Internet, GPS, even LLMs themselves, would not have been possible without developments in mathematical research that happened decades prior. Sometimes this research is directly out of necessity of solving a practical engineering problem, but it’s often just mathematicians intuitively noticing things and trying to prove whether they’re actually true or not. This is what Poincaré refers to as “the mathematician’s free initiative”.<br>When a mathematician “notices” something but is not sure whether it’s true, this is typically called a conjecture - think of it like a hypothesis. For example, in 1742, mathematician Christian Goldbach noticed that any even number could be written as the sum of two prime numbers or 1; e.g. 2 = 1+1, 6 = 3+3, 16 = 5+11, etc. It’s a simple statement most adults and even teenagers can understand. It even seems “intuitively true”; if we try to find an even number that can’t be written as the sum of two primes (or 1) we’ll struggle. In fact, we know it’s true up to a big (18-digit) number. But we surprisingly still haven’t proven - or disproven - Goldbach’s conjecture for all even integers. This kind of maths problem seems fun but ultimately useless, yet a huge part of the maths that led to the inventions and engineering wonders we use today comes from the process of trying to prove or disprove these seemingly innocuous statements.<br>This means that automating mathematical research will, in theory, significantly increase the pace at which technology, engineering, and other physical sciences evolve. The stakes are higher than they may initially seem.<br>How quickly AI is improving at maths

If we want to think about whether AI will replace mathematicians, it first helps to think about how quickly it improved recently, and where it is today.<br>I was part of a team helping train AI models to solve maths problems throughout 2024-25. Setting aside the moral dilemma between contributing to what may one day replace us mathematicians, and the excitement of contributing to the new age of the field, it was a particularly interesting exercise, and allowed me to experience the rate at which models were improving in mathematical reasoning firsthand, in depth, and 3-6 months before the general public. The way in which we’d train the models evolved slightly over time, but it was roughly:<br>Come up with a maths problem in a given subdomain with a clear solution or proof

Give it to a test model, which outputs its step-by-step reasoning (also known as “chain of thought” or “CoT”) and the final answer

The problem must be advanced enough that the model gets its chain of thought wrong, leading to an incorrect proof or final answer

Correct the chain of thought and final answer and send the result to the lab training the model (via an intermediary).

In mid 2024, it was pretty easy to “trick” those test models (which, presumably, were state-of-the-art at the time albeit not yet fully trained) into giving an incorrect answer to a high-school level problem. By early 2025, I was throwing the most creative graduate-level problems I could think of, and it was getting them...