AI can solve some very difficult math problems, but a striking contest result is not proof that a model is reliably good at all mathematics. The key distinction is between an answer that reads like a proof and a proof whose formal steps a computer can check. Even formal verification checks the statement as encoded, so a person still needs to judge whether that statement matches the original question.
Can AI solve math problems?
Yes, on some defined tasks—and recent International Mathematical Olympiad (IMO) results are meaningful evidence of progress. They are evidence about particular problems, systems, and evaluation conditions, not a general accuracy rate for AI mathematics.
| Evaluation | Reported result and conditions | What the result does—and does not—show |
|---|---|---|
| IMO 2024: AlphaProof and AlphaGeometry 2 | Google DeepMind reported a combined score of 28 of 42 points, in the silver-medal range. Experts manually translated the problems into formal language; AlphaProof searched for proofs in Lean, and the system did not solve either combinatorics problem. Google DeepMind’s 2024 account also describes some solutions as taking up to days. | A notable result using a formalized workflow, but not a direct natural-language, within-contest-time comparison with the following year. |
| IMO 2025: Gemini Deep Think | Google DeepMind reported that an advanced version earned 35 of 42 points by solving five of six problems perfectly. It says the system worked from the official natural-language statements within the official 4.5-hour limit, and that IMO graders assessed the solutions. Google DeepMind’s 2025 account quotes IMO President Gregor Dolinar describing the solutions as clear and precise. | Strong evidence of performance on that Olympiad under its stated conditions—not a measure of everyday accuracy, graduate research ability, or every model’s performance. |
| IMO-ProofBench Advanced, reported January 2026 | Google DeepMind reported up to 90% for a January 2026 Gemini Deep Think version as inference-time compute scaled; results were human graded. The same report says performance on PhD-level FutureMath Basic remained materially lower. Google DeepMind’s report describes these as distinct evaluations. | A benchmark result, not an official IMO score and not directly comparable with one. |
The 2024 and 2025 IMO results are not a controlled head-to-head: the systems used different workflows, including manual formal translation in 2024 versus the reported natural-language approach in 2025. Scores also depend on the exact problems, available time and compute, tools, prompting, and grading. Read the conditions alongside the headline number.
Can AI prove a theorem?
AI can produce candidate proofs, and some systems can work with proof assistants that check formal proof objects. Those are related but different claims. A persuasive natural-language explanation is not automatically a verified proof; a checked formal proof is evidence that the encoded proof follows the checker’s rules for the encoded statement.
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What Lean checks
Lean is an open-source proof assistant and theorem prover. Its system description identifies a small trusted kernel based on dependent type theory and describes Lean as supporting interactive and automated theorem proving. The Lean system description explains the foundations of this approach.
In practice, a proof assistant checks a formal object against formal rules. That can expose missing steps that a fluent explanation might conceal. But the kernel does not determine whether someone formalized the intended theorem, included appropriate assumptions, or answered the original informal question. The formalization itself remains part of the mathematical work.
What a formalization benchmark measures
The Lean AI formalization leaderboard focuses on hard formalization problems, generally with known informal solutions and statements that can mostly be expressed using Mathlib definitions. Its stated aim is correctness under comparator tests, not readability or reusable Lean coding practice. A strong score there therefore says something specific about that benchmark; it does not by itself establish broad theorem-proving ability.
Can AI make mistakes in math?
Yes. A proof can appear convincing while containing a subtle gap, and the harder the claim is to check by a short calculation or answer key, the more important independent scrutiny becomes. OpenAI’s January 2026 report on AI as a scientific collaborator discusses this failure mode and the role of Lean in requiring explicit steps under a formalization. OpenAI’s report does not make formal checking a substitute for judging whether the formal statement captures the intended problem.
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Research mathematics makes evaluation especially demanding: a result may require a long argument in a specialist area, and simple answer matching cannot establish that the argument is sound. In its February 2026 account of First Proof, OpenAI described ten research-level problems requiring end-to-end arguments. After expert feedback, it judged at least five attempts to have a high chance of correctness; several remained under review, and one attempt initially considered likely correct was later judged incorrect. OpenAI’s First Proof account also says the sprint used limited human supervision, suggestions to retry fruitful strategies, requests for clarification after feedback, and human selection among some attempts; the company said the process was not as controlled as it wanted.
In a separate account published October 6, 2026, OpenAI described mathematical results from an internal frontier model, including Lean formalizations for many proofs, reasoning summaries, attempted-problem statistics, and compute estimates. It reported that an average result used compute equivalent to roughly three hours of ChatGPT Pro thinking. That is OpenAI’s estimate for its described results, not a general cost figure or a comparable benchmark score. Read OpenAI’s account and its stated evaluation details.
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Google DeepMind’s January 2026 Aletheia report describes a research agent that generates candidate solutions, uses a natural-language verifier, revises or restarts in response to feedback, and can admit failure. It reports up to 90% on IMO-ProofBench Advanced as inference-time compute scales, with human grading; the same report shows materially lower performance on PhD-level FutureMath Basic. These publisher-reported results concern different evaluations and should not be treated as a single measure of research competence. See Google DeepMind’s Aletheia and benchmark account.
Across these examples, the available evidence does not establish a universal accuracy rate for AI mathematics, guarantee that a natural-language proof is correct, or provide a standardized comparison across all current models. Nor does it establish an independently replicated, broad measure of research-level mathematical competence.
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How do you check an AI-generated proof?
- Pin down the claim. Rewrite the problem precisely, including definitions, assumptions, domain restrictions, and what must be proved. Check that the model has not silently changed any of them.
- Ask for explicit reasoning. Request each inference, intermediate lemma, and calculation rather than only a polished final proof. Verify key steps independently; a longer explanation is not automatically a sound one.
- Test computational claims appropriately. Recalculate arithmetic and use a suitable tool where computation is part of the argument. A check of examples can reveal errors, but examples alone do not prove a general theorem.
- Use a proof assistant when feasible. Formalize the relevant statement and proof in Lean or another proof assistant, then make sure the formal statement faithfully represents the original question. A successful check supports the encoded proof, not every interpretation of the source problem.
- For research claims, inspect the full argument and evaluation. Seek expert review, including scrutiny of definitions, assumptions, novel steps, and any benchmark or selection process behind the claim.
How should you compare claims about AI math models?
There is no single score that captures mathematical ability across tasks. When reading a result, check what was evaluated and how:
- Task level: school exercises, Olympiad problems, formalization benchmarks, or specialist research problems.
- Input and output: natural-language questions and proofs, or formally encoded statements and proof objects.
- Verification: answer matching, human or expert graders, a proof-assistant kernel, a model-based verifier, or several of these.
- Resources: time limit, inference-time compute, external tools, retries, and parallel attempts.
- Human involvement: who translated or formalized the problem, prompted or guided attempts, selected among answers, revised work after feedback, and reviewed the result.
- Coverage and reproducibility: how many problems were used, where they came from, whether they were held out, whether proof artifacts are available, and whether independent experts can reproduce the assessment.
For example, the 2025 IMO announcement describes natural-language solutions within the official contest time limit, while the 2024 account describes expert translation into formal language and Lean-based proof search. That difference helps explain why the scores should not be presented as a controlled year-over-year test of the same system.
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