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AI has reached gold-medal-level performance on one International Mathematical Olympiad (IMO), and a company has now claimed its model solved the Navier–Stokes Millennium Prize problem. Those are very different kinds of evidence. The contest results show substantial progress on bounded mathematical problems; they do not establish that AI has taken over mathematical research.
Why AI’s math results are drawing attention
Mathematical ability is a high-profile test for AI because a convincing solution must do more than produce a plausible-sounding answer: it needs a chain of reasoning that can withstand scrutiny. Recent systems have made notable progress on competition problems, while new claims about research-level results have raised a harder question: how should mathematicians tell a real breakthrough from an impressive announcement?
The answer depends on what a system was asked to do, how much assistance and computation it used, what form its proof took, and who checked the result. An Olympiad score, a proof checked by software, and a claimed solution to a long-standing research problem are not interchangeable measures.
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What the 2024 IMO result actually involved
In the 2024 IMO evaluation, Google DeepMind combined two systems: AlphaProof and AlphaGeometry 2. Together they solved four of the six problems and scored 28 out of 42 points, a score within the silver-medal range and one point below the gold threshold. AlphaProof alone did not solve four problems: it solved three non-geometry problems, while AlphaGeometry 2 solved the geometry problem. The results are described in the Nature paper on Olympiad-level formal mathematical reasoning.
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AlphaProof’s formal-proof route
AlphaProof used reinforcement learning in Lean, a theorem prover. For the IMO evaluation, experts manually translated the five non-geometry problems into Lean. AlphaProof solved two algebra problems and one number-theory problem; the two combinatorics problems remained unsolved. Each of its three successful solutions required two to three days of test-time training, rather than only the contest’s usual working period.
The paper also reports that a Gemini model using Python generated candidate answers for several problems before AlphaProof verified correct candidates. That makes the result a significant demonstration of a combined system and workflow, not evidence that AlphaProof independently read every problem and solved it unaided in ordinary contest conditions.
Why the geometry result was separate
AlphaGeometry 2 handled the geometry problem. The four-problem total and 28-point score therefore describe the combined AlphaProof–AlphaGeometry 2 effort, not one general-purpose model. The distinction matters when interpreting headlines that compress the result into “AI solved four IMO problems.”
What changed at the 2025 IMO
Google DeepMind reported that an advanced version of Gemini Deep Think solved five of six problems at the 2025 IMO, earning 35 out of 42 points—gold-medal-level performance. The company said IMO coordinators officially graded and certified the solutions, which were produced from natural-language problem statements within the standard 4.5-hour contest time limit. Google DeepMind’s account is available in its announcement of the result.
Google described the system as using parallel thinking, reinforcement learning, a curated corpus of mathematics solutions, and prompt instructions with general hints. IMO President Prof. Dr. Gregor Dolinar, quoted in the announcement, said: “Their solutions were astonishing in many respects. IMO graders found them to be clear, precise and most of them easy to follow.” The official grading is meaningful evidence about the submitted contest proofs; the details about the system’s method come from Google’s description.
The two competitions are not a clean before-and-after test
| Result | System and proof route | Time and assistance | Reported outcome and check |
|---|---|---|---|
| IMO 2024 | AlphaProof plus AlphaGeometry 2. AlphaProof used Lean proofs; AlphaGeometry 2 solved the geometry problem. (Nature paper) | Experts manually formalized the five non-geometry tasks for AlphaProof; its three solved problems each took two to three days of test-time training. A Gemini model with Python also generated some candidate answers. (Nature paper) | Four of six problems; 28/42. Combined score reported by the Nature paper. |
| IMO 2025 | Advanced Gemini Deep Think, working from natural-language problem statements. (Google DeepMind) | Google said solutions were generated within the standard 4.5-hour contest limit; the company described parallel thinking, reinforcement learning, a curated solution corpus, and general-hint prompts. | Five of six problems; 35/42. Google said IMO coordinators graded and certified the solutions. |
These results show progress, but they are not identical experiments. The systems, interfaces, tool use, time allowances, proof formats, and evaluation arrangements differed. A higher score in 2025 does not, by itself, quantify how much better one system is at mathematical research or show that the same capabilities transfer to open-ended work.
Why an Olympiad medal is not a research takeover
An Olympiad asks contestants to solve a fixed set of difficult problems within a defined format and deadline. Mathematical research is less bounded: choosing a worthwhile question, developing concepts, finding useful connections, checking a proof, and explaining why a result matters can all be part of the work. A system can perform impressively on a contest without demonstrating that it can independently carry out this broader process.
Proof verification also has different meanings in the two results. A proof encoded and checked in Lean has been checked against the formal statement that was entered into the system. Human formalization is therefore part of the evidence: the Nature paper’s experts had to translate the non-geometry problems into Lean. At the 2025 IMO, the evidence described by Google was that human contest graders assessed the submitted natural-language solutions. Neither kind of check alone demonstrates that a system can autonomously select and advance a research program.
For a claimed research breakthrough, readers also need enough proof detail for mathematicians outside the announcing organization to scrutinize and reproduce the argument. The contest announcements and evaluations described here do not establish broad automation of research tasks, an effect on mathematics jobs, or replacement of professional mathematicians.
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What to make of the Navier–Stokes claim
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. This is an OpenAI claim, not an independently established resolution: the reviewed announcement does not establish an external mathematical assessment or recognition of the Navier–Stokes result by the Clay Mathematics Institute. It should not be reported as a settled solution.
OpenAI also said it would establish an independent mathematics advisory group. The company described the group’s role as advising on how to review and communicate emerging results, assess their significance, coordinate dissemination, and meet academic and professional standards. That plan does not itself verify the reported proofs. The announcement is at OpenAI’s page about its mathematics and AI advisory group.
The distinction is not that a company’s claim must be false, but that an announcement is not a substitute for mathematical review. Until the proof and its assessment can be independently examined, the accurate wording is that OpenAI says its model solved the problem.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Why mathematicians are debating the risks
The Leiden Declaration on Artificial Intelligence and Mathematics presents a set of concerns about how AI may change mathematical practice. It reflects a community position, not a claim that every mathematician agrees. The declaration says it reflects AI and mathematical practice as of May 2026 and followed a September 2025 Lorentz Center conference attended by around 60 participants from 10 countries, then eight months of working-group development.
Proofs that look right but are wrong
The declaration warns: “Current automated techniques can produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs.” A fluent explanation may be persuasive without being valid, so reviewers can face additional work separating sound reasoning from errors. Formal proof tools can help check a proof encoded in a formal system, but they do not erase the challenges of translating human mathematical ideas into that system or ensuring the formal statement captures the intended claim.
Credit, access, and research priorities
The declaration also raises questions about attribution, copyright and licensing, unequal access to systems, academic incentives, publicity arriving before research evaluation, and industry influence over which problems receive attention. These concerns are about more than whether a particular answer is correct: they ask who gets credit, who can use powerful tools, and how their use may shape the field.
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Outbyte PC Repair FREEClear out junk files and repair common Windows errorsFree Scan →Outbyte Driver Updater FREEScan for outdated or missing drivers - takes under a minuteDriver Scan →Its signatories include mathematicians and AI researchers. Terence Tao, a UCLA professor, endorsed the declaration with this observation: “The goal of mathematical research is human understanding of mathematics, and so mathematics can only thrive in a community of human mathematicians.” That view puts the goal of research in context: producing a correct answer can matter, but so can understanding the argument and how it connects to other mathematics.
How to judge the next “AI solved it” headline
Before treating a new result as evidence of a mathematical takeover, check what the system actually did and how the result was evaluated:
- Task: Was it a fixed contest problem or an open research question?
- Proof format: Was the proof formally checked, judged by human graders, or only presented by the organization making the claim?
- Human and tool input: Did people translate the problem, supply hints, curate training material, or use external tools as part of the workflow?
- Time and computation: Did the system work under contest conditions, or use extended test-time training and computation?
- Independent scrutiny: Can mathematicians outside the organization inspect the proof and its assumptions, and is there evidence of independent review?
- Research contribution: Does the result deepen understanding or open a path to further work, or does the evidence establish only a solution to one bounded problem?
- Openness and governance: Are the methods and results available for scrutiny, and who controls access, credit, and the choice of problems?
These questions explain why two high-scoring systems can provide materially different evidence. AlphaProof’s formalized IMO work and Gemini Deep Think’s human-graded natural-language solutions are both meaningful achievements, but neither contest result settles what AI can do across mathematical research. The later Navier–Stokes announcement makes the standard for careful attribution even more important: a remarkable claim should remain a claim until its proof and evaluation support a stronger conclusion.
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