Since 1959, the International Mathematical Olympiad (often known as the “IMO”) has been the most prominent math competition in the world for young mathematicians. Six top-tier pre-university mathematicians from each participating nation compete to solve six incredibly challenging problems in number theory, geometry, algebra, and combinatorics. The top half of competitors receive medals, with about 8% taking home the coveted gold medal.
The IMO has recently evolved into an ambitious challenge for AI systems, putting their sophisticated mathematical reasoning and problem-solving skills to the test. The combined Alpha Proof and Alpha Geometry 2 algorithms from Google DeepMind won the silver medal last year after scoring 28 points and resolving four of the six tasks. This innovation showed that AI was starting to resemble highly skilled human mathematical thinking by utilizing specialized formal languages.
This year, we were one of the first cohorts to have IMO coordinators formally grade and certify our model outcomes based on the same standards as student solutions. In light of the noteworthy achievements of this year’s student participants, we are thrilled to announce Gemini’s historic performance.
Breakthrough Performance at IMO 2025 with Gemini Deep Think
Five of the six IMO questions were completed flawlessly by an enhanced version of Gemini Deep Think, which received 35 points overall and performed at the gold medal level. The answers are available online at this link.
This accomplishment represents a substantial improvement above the ground-breaking outcome from the previous year. In order to use Alpha Geometry and Alpha Proof at IMO 2024, specialists had to first convert natural language problems into domain-specific languages like Lean, and then the proofs back into plain language. Additionally, the computation took two to three days. This year, inside the allotted 4.5 hours for the competition, our sophisticated Gemini model ran end-to-end in natural language and generated exacting mathematical proofs straight from the official problem descriptions.
