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Not yet. AI systems have reached elite olympiad performance: AlphaProof and AlphaGeometry 2 scored 28 of 42 points on the 2024 International Mathematical Olympiad (IMO), equivalent to a silver medal, and Google reported that Gemini Deep Think scored 35 points on the 2025 IMO, at gold-medal standard. Those results show that models can solve hard problems, but they do not show that AI can independently choose valuable research questions, develop useful mathematical concepts, or judge which discoveries matter. A machine-checked proof can establish that a particular formal statement follows from encoded rules; a fluent, unchecked explanation cannot offer that same guarantee.
What does it mean for AI to prove a theorem?
“Prove” can mean two quite different things in this context. An AI may generate a convincing natural-language argument for a claim, or it may produce a proof in a formal language that a proof assistant can mechanically check. The second result gives stronger evidence of correctness—but only for the statement that was actually encoded and under the rules and definitions the system was given.
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A natural-language solution may read cleanly while hiding an invalid inference, an unstated assumption, or a gap between steps. Google DeepMind warned in its 2024 AlphaProof announcement that natural-language approaches can hallucinate plausible but incorrect intermediate reasoning and solutions. Coherence is a useful sign that an answer deserves examination; it is not a correctness certificate.
That distinction remains important even when systems perform impressively. A 2025 paper in Nature describes rigorous verification of reasoning without a reference solution as an active research challenge. A solution to a problem is not automatically trustworthy merely because a model supplies a confident derivation or because the answer matches an expected result.
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What a proof assistant checks
Lean is a proof assistant: it checks whether a proof term follows from a theorem statement, definitions, and rules represented in its formal system. If the encoded proof passes that check, the system has verified the formal derivation. DeepMind described the central benefit of formal languages this way: “proofs involving mathematical reasoning can be formally verified for correctness.”
Mechanical checking is powerful, but it has a boundary. It does not by itself establish that the encoded theorem captures the informal question a mathematician intended, that the chosen definitions are useful, or that the result is important. Those are separate tasks involving interpretation and mathematical judgment.
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What have reasoning models actually proved?
The strongest results in the evidence here are in olympiad problem solving and bounded formal domains. They demonstrate that AI can find rigorous proofs in selected settings, but the numbers measure performance on particular tests—not general autonomy as a research mathematician.
2024 IMO: silver-medal-level score using two systems
Google DeepMind’s AlphaProof and AlphaGeometry 2 solved four of the six problems on the 2024 IMO and scored 28 of 42 points, a score equivalent to a silver medal. AlphaProof solved three of the five non-geometry problems; AlphaGeometry 2 solved the geometry problem. The result was reported in Nature in 2025.
This achievement came with significant setup and computation. Experts formalized the IMO problems for the systems, and the hardest problems required two to three days of computation. The result therefore combines model capability with human preparation and much more time than competitors had during the contest. It is strong evidence that the systems can solve selected difficult problems, not a like-for-like demonstration that they can independently do the work of a mathematician under ordinary research conditions.
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2025 IMO: a reported gold-medal-standard result
Google reported that Gemini Deep Think solved five of six problems on the 2025 IMO, earning 35 points at gold-medal standard. Unlike the 2024 pipeline, the result was reported as being produced directly in natural language within the contest’s 4.5-hour limit. It is a major capability result, but the claim should be understood as Google’s report; the evidence cited here does not establish independent verification beyond that official account.
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The 2024 and 2025 results should not be collapsed into a single claim that “AI has become a mathematician.” They involved different systems, approaches, time conditions, and verification arrangements. Both show unusually strong problem solving on a selective competition, while neither tests the full cycle of mathematical research.
Other benchmark figures have narrower meanings
In a 2024 Nature paper, Trinh and colleagues reported that AlphaGeometry solved 25 of 30 olympiad-level geometry problems. This is evidence about geometry problem solving, not about all branches of mathematics or research practice.
Stanford HAI’s AI Index Report 2025 reported that fully automatic systems solved 89% of problems in TPTP version 9.0.0, a formal-theorem-proving benchmark. “Fully automatic” distinguishes those systems’ benchmark setting from workflows requiring a human to formalize a new problem first. A high result on a fixed formal benchmark does not demonstrate that a model can select significant open questions or formulate the mathematics needed to address them.
How does AI find a proof, and where do people still have to help?
Reasoning systems combine ways of proposing a route to a result with ways of checking or exploring that route. The details differ: AlphaProof searched for proofs in Lean, while AlphaGeometry used a neural model to guide symbolic deduction in Euclidean geometry. Neither approach removes the need to represent the problem in a form the system can use.
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Formalization turns a human problem into a machine-checkable one
A mathematician can state a problem in ordinary language, diagrams, notation, and context. A proof assistant needs precise definitions and a statement expressed in its formal language. Someone must decide what objects and assumptions the problem refers to, encode them correctly, and make them available in the system’s environment.
This translation can be substantial work. The 2024 AlphaGeometry paper in Nature identifies the cost of translating human proofs into machine-verifiable form as a challenge for machine-learning systems, particularly in geometry. The 2024 AlphaProof pipeline likewise relied on experts to formalize the IMO problems. A model’s ability to finish a formal proof should therefore be distinguished from its ability to create the formal problem representation from an informal prompt.
Libraries and search shape what the system can reach
Formal proof work takes place within a system of definitions, previously established results, and rules. The available library affects what has already been expressed in a reusable form; a proof searcher must find a route through the material it can access. If a needed concept or result is absent or represented in a way the system cannot use, the task may involve adding or adapting formal mathematics before proof search can succeed.
AlphaProof’s approach used reinforcement learning to search for Lean proofs. AlphaGeometry’s approach used a neural model to guide symbolic deduction in Euclidean geometry. These are not interchangeable general-purpose techniques: one is described as formal proof search, the other as a geometry-focused system pairing learned guidance with symbolic reasoning. Results in one domain do not establish equal capability in another.
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In the 2024 IMO work, the hardest problems took two to three days of computation. That resource demand matters when judging practical use: solving a selected problem eventually is different from solving it quickly, economically, or reliably enough to support a researcher’s daily work. The 2025 Gemini Deep Think report, by contrast, gives a 4.5-hour contest window. The different conditions are useful context, not a direct efficiency comparison across systems.
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How should you judge whether AI is becoming a mathematician?
A contest medal or a benchmark percentage answers only a slice of the question. A serious assessment needs to separate at least four dimensions: whether a result is formally correct, how broadly the system works, whether it can help discover worthwhile mathematics, and how much human preparation and computation the result requires.
| Dimension | What a strong result would show | What the current evidence establishes |
|---|---|---|
| Formal correctness | A proof checker accepts a derivation of the intended statement under the intended definitions. | Lean can mechanically check proofs encoded in its formal system. Natural-language text alone is not a comparable check. |
| Breadth | Reliable work across mathematical areas, representations, and levels of difficulty. | The cited results are strong in selected olympiad, geometry, and formal benchmarks. They do not demonstrate equal ability across mathematics. |
| Discovery and problem choice | Identifying valuable questions, inventing useful definitions, and producing results whose significance can be understood. | The cited benchmark results do not establish autonomous performance on this broader research workflow. |
| Efficiency and setup | Useful output with manageable human preparation, tool dependence, and compute time. | The 2024 IMO pipeline required expert formalization and, for hard problems, two to three days of computation. |
There is also a difference between proving a claim and doing mathematics around it. Research involves deciding which questions are worth asking, noticing connections, choosing definitions that illuminate a subject, checking whether an approach is fruitful, and explaining what a result changes. A proof engine can contribute to parts of this process without replacing the judgment that organizes it.
Can AI-generated proofs be trusted?
Trust depends on the kind of output. A Lean proof accepted by the checker is strong evidence that the formal statement follows from the encoded assumptions; an unchecked natural-language proof remains something that a person or a reliable verification process must scrutinize.
For a formal proof
- Confirm that the theorem statement faithfully represents the intended mathematical claim.
- Check the assumptions, definitions, and relevant formal environment, not just the fact that the proof tool accepted a term.
- Keep the scope of the result precise: verification establishes the encoded derivation, not the broader significance of the theorem.
For a natural-language solution
- Inspect each inference, especially steps that say something is “obvious,” divide by a quantity, assume a case is exhaustive, or appeal to a named result.
- Look for hidden conditions, including domain restrictions and exceptional cases.
- Seek independent checking when the result matters; a persuasive answer is not a substitute for verification.
The central reliability question is not simply whether AI can produce a proof-shaped answer. It is whether the claim is precisely stated, the reasoning is valid, the result has been checked by an appropriate method, and the checking covers the claim the reader actually cares about.
Will AI replace mathematicians?
The evidence supports AI as a proof-search and mathematical-assistance tool, not as a replacement for mathematicians across research. Systems can solve difficult, well-specified problems and can produce proofs that a formal assistant checks. The cited results do not show that they autonomously choose significant research questions, invent broadly useful concepts, sustain a research collaboration, or assess the importance of a discovery.
That distinction does not diminish the achievements. Reaching silver-medal-equivalent performance on the 2024 IMO and a reported gold-medal-standard score on the 2025 IMO are substantial demonstrations of capability. They answer “Can AI solve hard mathematical problems?” with a qualified yes. They do not answer “Can AI replace the human work that decides what mathematics to pursue and why?” with yes.
For readers evaluating future claims, look beyond the headline score. Ask whether the result was formally checked or presented in natural language, which mathematical area it covers, how much human formalization it required, how long and how much computation it used, and whether the task tested discovery or only solution of supplied problems. Those details determine what a result says—and what it does not say—about AI and mathematical work.
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Can AI grade a mathematical proof?
It can help assess proofs, but grading is not the same as mechanically verifying a formal derivation. Stanford HAI’s AI Index Report 2026 reported Pearson correlations of 0.96 on basic and 0.93 on advanced proof grading in IMO-ProofBench; correlation describes agreement with grading judgments, not a guarantee that every assessment is correct.
Can AI solve unsolved mathematical problems?
The cited results do not establish that reasoning models can autonomously solve important open problems. They concern selected competition tasks and formal benchmarks, so they should not be read as evidence that AI has made a general breakthrough on unsolved research questions.
What is the difference between a proof benchmark and mathematical research?
A benchmark evaluates performance on a defined set of tasks, often with known statements and scoring rules. Research also requires deciding which questions matter and interpreting how a result changes a field—activities the reported benchmark scores do not measure.
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