AI Is Solving Open Math Problems. What Happens to Mathematicians and Their Tools?

What happened#

For years, AI proving a theorem was a demo. In 2026 it became research. In May, an OpenAI model disproved a famous conjecture of Paul Erdős about distances between points in the plane, and human mathematicians improved on the construction within weeks. Hobbyists with public chatbots had already been knocking down smaller Erdős problems since January. Then came September.

OpenAI says it turned its model on the Millennium Prize Problems after rumors that a rival had solved two. On September 8 it claimed a result on the Navier–Stokes problem. The Clay Mathematics Institute has not accepted it. On October 6 OpenAI posted the largest batch yet.

manuscripts posted on GitHub

~720

families of open problems

372

problems the model tried

~4,000

of headline results with a Lean proof

~42%

What is actually verified#

Less than the headlines suggest. OpenAI's own repository says the results sit at different stages of verification and that some unformalized ones could contain errors. About 42 percent of the headline results have a machine-checked proof in Lean, and a Lean proof only helps if it proves the statement the paper claims. Reporters and mathematicians have already found formalizations that look weaker than the claims they accompany.

OpenAI says each result took about three hours of compute on average. Tristan Buckmaster of NYU says that figure left out failed attempts and earlier agent work, which makes it close to meaningless. The Navier–Stokes claim also came with a dispute over credit, which OpenAI denies.

What mathematicians are saying#

Opinions fall into three camps. We have summarized each person's position in our own words and linked the source so you can read them directly.

Golden age or dark age?#

The mathematician Francesco Maggi framed the stakes on Tao's blog with two scenarios. In both, output rises sharply. They differ in who understands what is produced.

Maggi expects a mix of both, and argues the outcome depends on choices, not capabilities. He also argues society will need more mathematicians, not fewer. Buckmaster makes a related point through chess. Engines did not kill chess. They made top-level preparation available to far more people. What ended, in his view, is the race to be first to solve a famous problem, not the subject.

What changes for mathematicians#

The pressure points show up in everyday academic life. Here is what we see shifting, with a source for each.

What it means for the tools#

Mathematicians and engineers rarely work with a chat window alone. They work in exact tools, and those tools are adapting in three different ways.

Wolfram's own pitch is that language models are broad but imprecise, so they need an exact computation engine behind them. Its Foundation Tool is built around that idea. MATLAB is taking the editor route with an assistant inside the desktop. Lean sits at the other end, as the referee that decides whether a machine-written proof actually holds.

The research results themselves came from general frontier models, the same family you can try in ChatGPT, Claude and Gemini. If you are choosing between them for technical work, start with our ChatGPT vs Claude comparison.

Tool profileClaude on BettrListOur rating, plans and verdict for Claude.

Our view#

We write about software, not theorems, so we will stay modest about the mathematics. About the tools and the direction, we have four views.

1. Proofs are getting cheap. Understanding is not. A result nobody can read is a claim, not knowledge. The valuable work moves to explaining, checking and connecting results.
2. Verification is the real bottleneck. Writing a proof now costs less than establishing trust in it. That is why Lean, community review and slower, more careful publishing are suddenly central.
3. Exact tools move underneath. Mathematica, MATLAB and Lean do not compete with AI. They are the calculator the AI picks up and the referee that checks its work. Expect most of their growth to come from being called by agents.
4. Access is the open question. The Navier–Stokes claim reportedly needed thousands of agents for days, at a cost in the millions. Capability that large sits with a few labs, which is the same concentration we describe in our look at AI subscription pricing. Universities and individuals will feel it first.