AI can solve some difficult mathematics problems and produce proofs that experts judge impressive. But success on a defined contest or research challenge is not a guarantee that an AI model will get your next math question right. The key distinction is between an answer that sounds convincing and a proof whose steps have been checked—and even a formal checker can verify only the claim that was actually encoded.
Can AI solve math problems?
Yes, on some demanding problems. But a high score on a particular test is evidence about that test, not a universal measure of mathematical reliability. The result depends on the questions, time and compute allowed, tools, human assistance, and how answers are graded.
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The 2025 International Mathematical Olympiad
Google DeepMind reported that an advanced version of Gemini Deep Think earned 35 of 42 points at the 2025 International Mathematical Olympiad (IMO), solving five of the six problems perfectly. According to the company, the model worked from the official natural-language problem statements within the competition’s 4.5-hour limit, and IMO graders assessed its solutions. IMO President Gregor Dolinar said the solutions were “astonishing in many respects” and that graders found most clear, precise, and easy to follow. This is a notable result on Olympiad mathematics; it does not establish how reliably the model handles everyday calculations, other branches of mathematics, or open research questions. Google DeepMind’s 2025 IMO account
Why the 2024 result is not a head-to-head comparison
For the 2024 IMO, Google DeepMind reported that its combined AlphaProof and AlphaGeometry 2 system scored 28 of 42 points, in the silver-medal range. Experts manually translated the problems into formal language; AlphaProof searched for proof steps in Lean, and the system did not solve either of the two combinatorics problems. DeepMind also said that some solutions took up to days. The 2024 and 2025 scores came from different systems and workflows, so they should not be read as a controlled comparison of model capability. Google DeepMind’s 2024 IMO account
#1 Best Overall
| Evaluation | Reported result | Input and workflow | What the result shows |
|---|---|---|---|
| 2024 IMO, AlphaProof and AlphaGeometry 2 | 28 of 42 points, reported by Google DeepMind | Experts manually translated problems into formal language; AlphaProof used Lean proof search. DeepMind reported that some solutions took up to days. | Performance on that contest under a formal-translation pipeline—not a natural-language, within-contest-time result. |
| 2025 IMO, advanced Gemini Deep Think | 35 of 42 points and five problems solved perfectly, reported by Google DeepMind | Natural-language official statements; the official 4.5-hour time limit; IMO graders reviewed the solutions. | A strong result on that Olympiad evaluation—not a general accuracy rate for AI mathematics. |
For either result, a useful comparison asks what task was set, what the model received and returned, how it was checked, how much time and compute it used, and how much human translation, prompting, selection, or review was involved.
Can AI prove a theorem?
AI systems can produce candidate arguments, and some can work with formal proof systems. “Prove” can mean different things, though: a fluent natural-language explanation is not automatically a verified proof, while a formally checked proof applies only to its encoded theorem and assumptions.
What Lean checks
Lean is a proof assistant: mathematics is expressed in a formal language, and a computer checks whether a proof object follows the system’s rules for the formal statement. Lean’s system description identifies a small trusted kernel based on dependent type theory and describes support for interactive and automated theorem proving. Lean’s system description
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A successful check is strong evidence that the encoded proof follows the rules. It does not, by itself, establish that the formal statement faithfully captures the informal problem, that its assumptions are appropriate, or that the theorem is an important or novel result. Formalization is part of the mathematical work, not a detail that can be skipped.
Rank #3
What a formalization benchmark measures
The Lean AI formalization leaderboard focuses on hard formalization problems that are generally expressible with Mathlib definitions and usually have known informal solutions. Its stated emphasis is correctness under comparator tests, not readability or reusable Lean coding practice. A result on that leaderboard therefore answers a narrower question than “Can this model do mathematics?” Lean AI formalization leaderboard
Can AI make mistakes in math?
Yes. A model can make a computational error, rely on an unstated assumption, misread the question, or produce an argument with a subtle gap. Polished mathematical language is not evidence that each inference is valid. OpenAI’s January 2026 account of AI as a scientific collaborator discusses the familiar problem of arguments that appear sound but contain subtle errors, and describes Lean checking as a way to require explicit steps under a stated formalization. OpenAI’s January 2026 report
Rank #4
Research problems make evaluation harder than checking a short answer. OpenAI’s February 2026 report on the First Proof challenge describes ten specialist, research-level problems that required end-to-end arguments. After expert feedback, OpenAI said at least five attempts had a high chance of correctness; several others remained under review, and one attempt initially viewed as likely correct was later judged incorrect. The process included limited human supervision, suggestions to retry fruitful approaches, requests to clarify arguments after feedback, and human selection among some attempts; OpenAI said the sprint was not as controlled as it wanted. These qualifications matter when interpreting the reported outcomes. OpenAI’s First Proof account
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Newer research claims need their own context
In January 2026, Google DeepMind described Aletheia, a research agent that generates candidate solutions, uses a natural-language verifier, revises or restarts in response to feedback, and can acknowledge failure. DeepMind reported up to 90% on IMO-ProofBench Advanced for a January 2026 version as inference-time compute scaled, with results human graded. Its reported performance on PhD-level FutureMath Basic was materially lower. These are publisher-reported results on distinct evaluations, not a directly comparable official IMO score or a broad guarantee of research-level correctness. Google DeepMind’s January 2026 account
Best Value
In October 2026, OpenAI published mathematical results from an internal frontier model, including Lean formalizations of many proofs, reasoning summaries, attempted-problem statistics, and compute estimates. OpenAI estimated that the average result used compute equivalent to roughly three hours of ChatGPT Pro thinking. That is the company’s estimate for the described results, not a general cost measure or a score directly comparable with the contest and benchmark results above. OpenAI’s October 2026 account
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How do you check an AI-generated proof?
Match the checking method to the claim. For a calculation, check the arithmetic and assumptions; for a proof, inspect the logical steps; for a formal result, check the encoded theorem and proof. For a research claim, also seek expert scrutiny of the mathematics and the evaluation process.
- Pin down the question. Confirm the definitions, assumptions, domain, and requested conclusion. Ask the model to state any assumptions it is using.
- Ask for explicit reasoning. Request intermediate steps and the justification for each non-obvious inference. Check the steps rather than relying on a confident final answer.
- Verify calculations independently. Recompute consequential arithmetic and test computational claims with suitable tools. A computational check can test examples or calculations; it does not alone prove a general theorem.
- Use a proof assistant when appropriate. Formalize the key statement and proof in Lean or another proof assistant if you can. A successful check supports the formal proof, but you must still assess whether the formalization represents the original question.
- For research-level claims, inspect the argument and evaluation. Look for the full proof, its assumptions, expert review, human involvement, and how the result was graded. A benchmark score or model-generated summary is not a substitute for this scrutiny.
What AI math results do not establish
The reported demonstrations do not establish a universal accuracy rate for AI mathematics, a guarantee that natural-language proofs are correct, or a standardized ranking across all current models. Nor do the cited results provide an independently replicated, broad measure of research-level mathematical competence. Treat each score as evidence about the specific problems, method, resources, and review process behind it.
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1Clear out junk files and repair common Windows errors2Fix the driver behind crashes, sound loss and screen glitches3Repair Windows errors before they cause bigger problemsWhere AI is useful in mathematical work
AI can be useful as an assistant for exploring possible approaches, suggesting candidate lemmas, explaining concepts, or drafting a proof outline. Those uses can help a person make progress without making the model the authority on correctness. When an answer matters, independently verify the calculations and assumptions, ask for explicit steps, and use formal checking when feasible. For a research claim, examine the actual proof and seek expert review.
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