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Outbyte PC Repair FREERepair Windows errors before they cause bigger problemsFix Now →Outbyte Driver Updater FREEScan for outdated or missing drivers - takes under a minuteDriver Scan →AI systems have reached gold-medal-level performance on an International Mathematical Olympiad (IMO) contest, and OpenAI has claimed a new model solved the Navier–Stokes Millennium Prize problem. Those are very different kinds of evidence. The Olympiad results show substantial progress on tightly defined problems; they do not establish that AI can independently replace mathematicians or conduct broad mathematical research.
What the AI mathematics results actually show
Two prominent IMO results have fueled talk of a takeover, but they came from different systems and used different methods. Google DeepMind’s 2024 result combined AlphaProof with AlphaGeometry 2. Its 2025 result was reported for an advanced version of Gemini Deep Think. Neither score should be read as a direct measure of how much mathematical research AI can do.
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| Result | Problems and score | How the solutions were produced and checked |
|---|---|---|
| IMO 2024: AlphaProof and AlphaGeometry 2, reported in a 2025 Nature paper | Four of six problems; 28 of 42 points, within the silver-medal range and one point below the gold threshold. | AlphaProof worked in Lean, with experts manually formalizing the five non-geometry problems. AlphaGeometry 2 solved the geometry problem. AlphaProof’s three solutions each took two to three days of test-time training. The paper also reports that a Gemini model using Python generated candidate answers for several problems before AlphaProof verified correct candidates. Nature paper |
| IMO 2025: advanced Gemini Deep Think, according to Google DeepMind | Five of six problems; 35 of 42 points, a gold-medal-standard score. | Google DeepMind says the system received natural-language problem statements and produced proofs within the standard 4.5-hour contest limit. The company says IMO coordinators officially graded and certified the solutions. Google DeepMind’s announcement |
The scores are comparable as contest outcomes, but the experiments are not identical. One involved Lean formalization, multiple systems and computation over days; the other, as described by Google DeepMind, used natural-language inputs and the contest time limit. A score without those conditions strips away important context.
Why the 2024 AlphaProof result is not a single-system sweep
AlphaProof did not solve four of the six IMO problems by itself. In the Nature paper’s account, experts translated the five non-geometry problems into Lean, a proof assistant that checks whether a formal proof follows from its stated assumptions. AlphaProof solved two algebra problems and one number-theory problem; it did not solve the two combinatorics problems. AlphaGeometry 2, a separate system, solved the geometry problem.
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The paper also describes a role for a Gemini model with Python tools: it produced candidate answers for some tasks, which AlphaProof then verified. That makes the result a meaningful achievement in a tool-assisted system pipeline, not evidence that AlphaProof independently read, solved and proved every problem unaided. Lean checking is strong evidence that a formalized proof is valid within the formal system; it does not erase the human work of translating the original problem or the assumptions involved in that translation.
What the 2025 Gemini result adds—and what it does not
Google DeepMind says its advanced Gemini Deep Think system solved five of six IMO 2025 problems for 35 points. Unlike the 2024 AlphaProof setup, the company says this system received the problems in natural language and generated proofs during the 4.5-hour contest session. Google describes its approach as using parallel thinking, reinforcement learning, a curated corpus of mathematics solutions and prompt instructions containing general hints.
Google DeepMind also says IMO coordinators graded and certified the proofs. IMO president Gregor Dolinar, quoted in the company’s announcement, said: “Their solutions were astonishing in many respects. IMO graders found them to be clear, precise and most of them easy to follow.” That is significant evidence of strong performance on a demanding, bounded contest. It is not the same verification pathway as a proof assistant checking a formal proof, and neither pathway alone establishes that the system can originate and sustain a research program.
Why an Olympiad medal is not a research takeover
Olympiad problems are difficult, but the task is defined: contestants receive a fixed set of questions, have a fixed time, and are judged on solutions to those questions. Mathematical research also involves deciding which questions matter, locating useful connections, developing and revising conjectures, producing proofs other mathematicians can scrutinize, and explaining why a result advances understanding. Contest results do not measure that full range of work.
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- Task: solving a known contest problem is different from identifying a fruitful open question.
- Proof pathway: Lean verification of a formalized statement and human grading of a natural-language proof test different things.
- Support and constraints: human formalization, tools, hints, curated data, compute and time limits affect what a system has demonstrated.
- Research validation: a contest score is not an independent review of a research result, its importance or its reproducibility.
- Understanding: producing a correct answer does not by itself show that a system can explain its significance or contribute reliably to the wider development of mathematics.
The reviewed contest results offer no basis for a general claim about how many professional research tasks AI has automated, or whether mathematicians’ jobs are being displaced. They establish specific capabilities under specific evaluation conditions.
What is behind the mathematicians’ concern
The Leiden Declaration on Artificial Intelligence and Mathematics, published in 2026, sets out concerns held by its signatories; it should be understood as a community position, not a finding that every mathematician shares. It followed a September 2025 Lorentz Center conference attended by around 60 participants from 10 countries and eight months of subsequent working-group development.
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The declaration argues that automated systems can produce plausible but incorrect arguments that are hard to distinguish from valid proofs. Formal methods can help check proofs, but translating between computer-encoded statements and human mathematical concepts can itself be difficult. The declaration also raises questions about attribution, copyright and licensing, unequal access to systems and decision-making, academic incentives, publicity that precedes research evaluation, and the influence of companies over which problems receive attention.
These concerns do not cancel out the technical progress. They point to a broader issue: a system’s output can be useful, impressive or even correct while the mathematical community still needs to establish how it was produced, who contributed, whether it can be checked and what it means for the field.
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How to assess claims that AI has solved a major open problem
On September 21, 2026, OpenAI announced that a new internal model, which it said had been training since August 28, solved the Navier–Stokes Millennium Prize problem and more than 100 other long-standing problems. The announcement also said OpenAI would establish an independent mathematics advisory group to advise on the significance and communication of emerging results and on academic and professional standards. These are claims by OpenAI; the announcement does not establish an independent mathematical assessment or recognition of the Navier–Stokes result by the Clay Mathematics Institute. OpenAI’s announcement
For a claim of this scale, the useful questions are not just whether a model produced a proof, but what independent mathematicians have checked and what is publicly available for scrutiny:
- Is the full proof or enough detail to assess it publicly available?
- Have independent experts checked the argument, including the technical steps and assumptions?
- Can other researchers reproduce the result or verify a formal proof where one is provided?
- Is the claimed result accepted by the relevant mathematical community or prize authority, if applicable?
- Does the report distinguish the model’s contribution from human guidance, tools and other methods?
Until those questions have answers, an announcement of a solved problem is evidence of what the organization claims, not proof that the mathematical community has accepted the result.
What “takeover” would require us to establish
A strong competition score is a milestone, not a verdict on the future of mathematics. To judge whether AI is changing research rather than just excelling at selected problems, look for results that are independently reviewed, sufficiently documented for others to check, and clear about human input, tools and resources. Then ask whether the work helps mathematicians understand or advance a research area—not only whether it produces a correct answer.
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