Artificial Intelligence Takes on the Math Olympics

For four years, Trieu Trinh has been preoccupied with developing an A.I. model that can solve geometry problems from the International Mathematical Olympiad, a competition for high-school students with a strong interest in math. Dr. Trinh recently earned his doctoral degree from New York University and published his findings in Nature. His system, named AlphaGeometry, can solve Olympiad geometry problems at a level very close to a human gold medalist.

While working on the project, Dr. Trinh presented his ideas to two Google scientists, who decided to bring him on board from 2021 to 2023. AlphaGeometry has joined Google DeepMind’s collection of A.I. systems, known for taking on significant challenges.

After presenting AlphaGeometry with a test set of 30 Olympiad geometry problems, the system solved 25 of them, which is similar to the average number of problems a human gold medalist solves. In comparison, another strong math-based system from the 1970s only solved 10 problems.

Google DeepMind has been pursuing numerous projects focused on the application of A.I. to mathematics, while Olympiad math problems have become a benchmark for broad research across various entities. Extra motivation comes from the I.M.O. Grand Challenge and the new Artificial Intelligence Mathematical Olympiad Prize, which offers a $5 million prize to the first A.I. to win Olympiad gold.

AlphaGeometry is a “neuro-symbolic” system, combining a neural net language model with a symbolic engine, custom-built for geometry. Dr. Trinh trained the neural net with algorithm-generated data, and once the system was set in motion to solve a problem, the symbolic engine initiated the solution process. Dr. Trinh is hoping to extend the system’s capabilities across various fields of mathematics and beyond.

While impressive, Dr. Luong believes that a visual component would add value to AlphaGeometry; he suggests that Google’s Gemini, a “multimodal” system, could incorporate both text and images into its reasoning.

Despite its success, some mathematicians believe that the beauty and soul of a solution is lacking in AlphaGeometry’s computational approach. Evan Chen, an I.M.O. coach and doctoral student at M.I.T., expressed curiosity about how the machine comes up with solutions, similar to his interest in understanding humans’ thought processes.

Overall, Dr. Trinh considers mathematical reasoning to be just one form of reasoning but emphasizes its importance in building a reliable A.I. for various applications.

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