AI Solves Olympiad Geometry

This is a big step toward creating robots with more sophisticated reasoning abilities than humans.

When tested on a set of thirty IMO geometry questions, AlphaGeometry was able to answer twenty-five of them.

This performance is almost on par with that of an IMO human gold medalist.

The system blends a symbolic deduction engine that verifies ideas using formal logic and rules with a neural language model that creates intuitive concepts.

AlphaGeometry uses its symbolic engine to first try and produce a proof when it is given a geometry problem. The language model adds a new point or line to the diagram if the symbolic engine is unable to solve the problem on its own. This gives the symbolic engine more options for solving the problem.

To construct AlphaGeometry, a bespoke language including several dozen fundamental geometry principles has to be created. The group then created a program that would automatically produce 100 million “proofs,” which were essentially arbitrary orders of easy-to-understand but logically sound procedures. These machine-generated proofs served as the training set for AlphaGeometry, which enabled it to solve issues by making successive guesses.

The system’s performance for geometry issues outperforms the prior state-of-the-art method, and it advances mathematical AI thinking.

Despite their progress, the researchers are aware of the shortcomings and difficulties in their work, including the need for more proofs that can be understood by humans and the ability to scale to increasingly difficult issues.