DeepMind reaches silver-medal level at the Math Olympiad

Google DeepMind has taken its mathematical reasoning systems to an unprecedented result at the International Mathematical Olympiad (IMO), the world’s most demanding competition for high school students. AlphaProof and AlphaGeometry 2 solved four of the six problems in the 2024 edition and scored 28 out of 42 points—a silver-medal score.

The gold-medal cutoff at this year’s competition was 29 points. The numerical gap may seem small, but the scale matters: this was not a single AI competing as a student under the usual conditions. It was two specialized systems tackling different problems, with their results evaluated according to IMO standards.

Four out of six problems, with verifiable proofs

Each Olympiad problem is worth seven points and requires a proof, not just the correct answer. DeepMind says AlphaProof solved two algebra problems and one number theory problem, while AlphaGeometry 2 solved the geometry problem. IMO coordinators graded the solutions using the competition’s scoring system.

That detail sets this achievement apart from many eye-catching results produced by language models. A chatbot can generate a convincing mathematical explanation and still contain a logical leap or an incorrect operation. AlphaProof works differently: it searches for proofs expressed in Lean, a formal language that allows every step to be verified by a program.

A formal proof is, in practice, a proof written in notation that a computer can check without ambiguity. If a condition is missing or a step does not follow from the preceding ones, the verifier rejects it. The trade-off is that the problem must first be translated into that formal language, a task that still requires mathematical and technical expertise.

From AlphaGo to theorem proving

AlphaProof builds on an idea DeepMind has used since AlphaGo: learning through reinforcement. Instead of choosing moves on a board, the system explores reasoning steps until it finds a sequence that concludes with a valid proof. The company trained it on large collections of formalized mathematical problems and generated new problems to expand that training.

AlphaGeometry 2 has a different design. It combines a neural model, useful for proposing geometric constructions and relationships, with a symbolic engine that applies explicit rules. That combination matters because Olympiad geometry often requires discovering an auxiliary idea—such as a line or circle not mentioned in the problem statement—and then chaining together exact deductions.

The result improves on the level DeepMind demonstrated with AlphaGeometry in early 2024. At the time, the system solved a significant share of historical IMO geometry problems; now the company is presenting a combined performance that approaches the competition’s top medal tier.

A genuine milestone, but not general-purpose mathematics

The comparison with a medal needs to be read carefully. Human participants receive the problems in natural language, have two days of exams, and write their answers without relying on a prepared formal translation. AlphaProof, by contrast, needs the problem to be expressed in Lean before it begins searching. DeepMind also divided the competition between systems designed for specific areas.

That is why the announcement does not show that an AI has the mathematical flexibility of an Olympiad contestant, much less that it can conduct research autonomously. It does demonstrate something important: AI methods can now produce rigorous proofs for problems that, until recently, were considered the domain of highly trained human reasoners.

The most immediate value lies beyond the Olympiads. Tools such as AlphaProof could help formalize theorems, detect errors in lengthy proofs, and assist researchers in fields where exact verification is crucial. The next challenge will be to reduce their reliance on manual formalization and help these systems better understand statements and mathematical ideas expressed in ordinary language.