An AI model has won a gold medal at the International Mathematical Olympiad (IMO) one of the world’s longest-running and most prestigious competitions for young mathematicians.
Each country taking part is represented by six elite, pre-university mathematicians who compete to solve six exceptionally difficult problems in algebra, combinatorics, geometry, and number theory. Medals are awarded to the top half of contestants, with approximately 8% receiving a prestigious gold medal.
Recently, the IMO has also become an aspirational challenge for AI systems as a test of their advanced mathematical problem-solving and reasoning capabilities. Last year, Google DeepMind’s combined AlphaProof and AlphaGeometry 2 systems achieved the silver-medal standard, solving four out of the six problems and scoring 28 points.
Making use of specialist formal languages, this breakthrough demonstrated that AI was beginning to approach elite human mathematical reasoning.
This year, Google DeepMind was among an inaugural cohort to have its model results officially graded and certified by IMO co-ordinators using the same criteria as for student solutions.
An advanced version of Gemini Deep Think solved five out of the six IMO problems perfectly, earning 35 total points, and achieving gold-medal level performance.
The solutions can be found online here.
“We can confirm that Google DeepMind has reached the much-desired milestone, earning 35 out of a possible 42 points — a gold medal score. Their solutions were astonishing in many respects. IMO graders found them to be clear, precise and most of them easy to follow,” says Professor Dr Grego Dolinar, president of the IMO.
This achievement is a significant advance over last year’s result. At IMO 2024, AlphaGeometry and AlphaProof required experts to first translate problems from natural language into domain-specific languages, such as Lean, and vice-versa for the proofs. It also took two to three days of computation.
This year, the advanced Gemini model operated end-to-end in natural language, producing rigorous mathematical proofs directly from the official problem descriptions – all within the 4,5-hour competition time limit.
It was achieved using an advanced version of Gemini Deep Think – an enhanced reasoning mode for complex problems that incorporates some of our latest research techniques, including parallel thinking. This setup enables the model to simultaneously explore and combine multiple possible solutions before giving a final answer, rather than pursuing a single, linear chain of thought.
To make the most of the reasoning capabilities of Deep Think, the Google team also trained this version of Gemini on novel reinforcement learning techniques that can leverage more multi-step reasoning, problem-solving and theorem-proving data. They also provided Gemini with access to a curated corpus of high-quality solutions to mathematics problems, and added some general hints and tips on how to approach IMO problems to its instructions.
This version of this Deep Think model will be made available to a set of trusted testers, including mathematicians, before rolling it out to Google AI Ultra subscribers.