The company says that it has created a new AI system that can solve geometry problems at the level of the very top high-school students.
Geometry is one of the oldest branches of mathematics, but has proven particularly difficult for AI systems to work with. It has been difficult to train them because of a lack of data, and succeeding requires building a system that can take on difficult logical challenges.
Typically, engineers train such systems using machine learning, which involves providing them with data on how to successfully complete a task, and have them learn how to do so. But there are few such human demonstrations available for proving theorems, especially in geometry.
Instead, researchers say they used a different approach to build the new system known as AlphaGeometry. They instead used a language model that was able to train itself by synthesising millions of theorems and their proofs, and then combined that with a system that can search through branching points in challenging problems.
Taken together, that system is able to learn and then solve complex geometrical problems without human input, the creators claim.
It was put to the test with 30 problems from the International Mathematical Olympiad, which is a competition in which the top-performing high school students are asked to prove mathematical theorems. AlphaGeometr was able to solve 25 of them.
That is far better than the previous best method, which was only able to solve 10 problems. It gets it close to the average gold medallist, who solved 25.9 theorems.
The system was also able to provide the proof in ways that humans understood – and even found a new version of one theorem, researchers said.
At the moment, the system can only be used on specific kinds of geometry. But it could eventually be used in different branches of mathematics, the researchers say.
While much of the focus of recent AI excitement has been on large language models such as ChatGPT, Deepmind has focused primarily on more practical uses of artificial intelligence. That includes recent breakthroughs in weather forecasting and other parts of mathematics, for instance.
The work is described in a new paper, ‘Solving olympiad geometry without human demonstrations’, published in Nature.