Google Deepmind says a new AI system has made a major breakthrough in one of the most difficult tests for AI.
The company says it has created a new artificial intelligence system that can solve geometry problems at the level of the best high school students.
Geometry is one of the oldest branches of mathematics, but it seems to be particularly difficult for AI systems to work on. Training them is difficult due to a lack of data, and success requires building a system that can tackle challenging logic problems.
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Engineers often train such systems using machine learning, which provides them with data on how to successfully complete a task and teaches them how to do it. But especially in geometry, there are very few examples that humans have come up with that can be accessed to prove theorems.
Instead, the researchers say they used a different approach to create the new system, called AlphaGeometry. They used a language model that can train itself by synthesizing millions of theorems and their proofs, and then combined this with a system that can search for inflection points in challenging problems.
Taken together, the creators claim, this system can learn and solve complex geometric problems without human input.
The system was tested with 30 problems from the International Mathematical Olympiad competition, where top-performing high school students were asked to prove math theorems. AlphaGeometry was able to solve 25 of them.
This is much better than the previous best method, which could only solve 10 problems. It also comes close to the average gold medalist who solved 25.9 theorems.
The system can also present evidence in a way that people can understand and even come up with a new version of a theorem, the researchers said.
Currently, the system can only be used in certain types of geometry. But the researchers say it could eventually be used in other branches of mathematics.
While much of the recent AI excitement has centered on big language models like ChatGPT, Deepmind is focusing primarily on more practical uses of AI. This includes weather forecasting, for example, and recent breakthroughs in other parts of mathematics.
The work is described in a new paper titled “Solving olympiad geometry without human demonstrations” published in the academic journal Nature.
