• Published Date and Authors: Published on 21 July 2025. Authors have an image and are likely from Google DeepMind.
• International Mathematical Olympiad (IMO): World's most prestigious competition for young mathematicians since 1959. Each country is represented by 6 pre-university mathematicians who solve 6 difficult problems in different fields. Medals are awarded to the top half, with 8% getting gold.
• AI and IMO: Recently, IMO has become a challenge for AI systems. Last year, Google DeepMind's AlphaProof and AlphaGeometry 2 systems achieved silver-medal standard by solving 4 out of 6 problems.
• Gemini's Breakthrough in 2025: An advanced version of Gemini Deep Think solved 5 out of 6 IMO problems perfectly, getting 35 points and achieving gold-medal level. The solutions are available online. This is a significant advance over last year, with the model operating in natural language within the 4.5-hour competition time limit.
• Using Deep Think Mode: Achieved this year's result using an advanced version of Gemini Deep Think with parallel thinking. Trained on novel reinforcement learning techniques and provided with a curated corpus of high-quality solutions and hints. Will make this model available to trusted testers.
• The Future of AI and Mathematics: DeepMind has ongoing collaborations with the mathematical community. This year's approach was based on natural language, but progress is also being made on formal systems. Combining natural language fluency and rigorous reasoning will be valuable.
• Acknowledgements: Thank many people and teams including those leading technical directions, providing technical leads, and offering various support and contributions. The IMO has confirmed the submitted answers are correct. The review doesn't validate the system, processes, or model.