To coach AlphaGeometry’s language model, the researchers needed to create their very own training data to compensate for the scarcity of existing geometric data. They generated nearly half a billion random geometric diagrams and fed them to the symbolic engine. This engine analyzed each diagram and produced statements about its properties. These statements were organized into 100 million synthetic proofs to coach the language model.

Roman Yampolskiy, an associate professor of computer science and engineering on the University of Louisville who was not involved within the research, says that AlphaGeometry’s ability shows a major advancement toward more “sophisticated, human-like problem-solving skills in machines.” 

“Beyond mathematics, its implications span across fields that depend on geometric problem-solving, comparable to computer vision, architecture, and even theoretical physics,” said Yampoliskiy in an email.

Nonetheless, there’s room for improvement. While AlphaGeometry can solve problems present in  “elementary” mathematics, it stays unable to grapple with the varieties of advanced, abstract problems taught at university.

“Mathematicians could be really interested if AI can solve problems which might be posed in research mathematics, perhaps by having latest mathematical insights,” said van Doorn.

Luong says the goal is to use an analogous approach to broader math fields. “Geometry is just an example for us to show that we’re on the verge of AI with the ability to do deep reasoning,” he says.