Google has developed a revolutionary artificial intelligence system that is capable of solving complex geometric tasks at the Olympiad level. According to an article published in the journal Nature, the system called AlphaGeometry successfully solved 25 out of 30 tasks from the International Mathematical Olympiad for the period from 2002 to 2022, which is almost equal to the results achieved by the best young mathematicians.
Previously, computer algorithms could solve no more than 10 such problems. In comparison, the bronze medalists at the Olympics solve an average of 19 problems, silver medalists solve about 23, and gold medalists solve 26. The test set for AlphaGeometry was compiled from the tasks of past years.
AlphaGeometry utilizes an innovative approach that combines fast and intuitive thinking. Firstly, the system includes a neural network that generates intuitive ideas for problem-solving. Secondly, there is a module of symbolic logical conclusions responsible for the strict substantiation of decisions according to rules.
The AlphaGeometry model was studied with 100 million unique examples, which were generated automatically without human intervention.
According to Evan Chen, a mathematics coach and former Olympics winner, the solutions provided by AlphaGeometry are very logical and easily checked. Unlike previous AI models, AlphaGeometry employs classical geometric rules with angles and similar triangles, just like students do.
Although the AlphaGeometry system has not yet reached the level of the Olympics, its capabilities allow it to surpass the bronze medal threshold achieved in 2000 and 2015. It is the world’s first AI system with this level of geometry skill. Google researchers note that AlphaGeometry demonstrates the increasing AI abilities in logical thinking and self-learning.
The code and model for AlphaGeometry have been made available in the public domain. This will enable mathematics and artificial intelligence specialists to utilize the technology’s achievements in their research and contribute to its further development.