Scientists at Google DeepMind, Alphabet’s advanced AI research division, have created artificial intelligence software able to solve difficult geometry proofs used to test high school students in the International Mathematical Olympiad.
This research, which was published today in the scientific journal Nature, represents a significant advance over previous AI systems, which have generally struggled with the kinds of mathematical reasoning needed to solve geometry problems.
Companies around the world, including Google DeepMind’s rivals at OpenAI and Anthropic, have been racing to try to endow generative AI systems with better reasoning and planning abilities, which are seen as crucial steps towards creating AI that can match human cognitive abilities across an even greater range of skills and tasks. They could also point the way towards AI systems that could not just mimic past examples, but puzzle out new scientific discoveries.
In late November, news reports surfaced that OpenAI researchers may have made a breakthrough in creating AI software that could learn to solve grade school mathematics problems it had not seen before in training. Even this modest achievement—which was reported based on anonymous sources and has not been confirmed by OpenAI—was enough to create a wave of excitement among AI researchers.
DeepMind’s new geometry-solving software combines two different approaches to AI and this sort of hybrid approach may be promising for addressing challenges in other domains—from physics to finance—that also require a combination of explicit rules and a more intuitive sense of how to apply those rules to solve a problem.
One component of the software, which DeepMind calls AlphaGeometry, is a neural network. This is a kind of AI, loosely based on the human brain, that has been responsible for most of the recent big advances in the technology. But AlphaGeometry’s other component is a symbolic AI engine, which uses a series of human-coded rules for how to represent data as symbols and then manipulate those symbols to reason. Symbolic AI was a popular approach to AI for decades before neural network-based deep learning took off began to show rapid progress in the mid-2000s.
In this case, the deep learning component of AlphaGeometry develops an intuition about what approach might best help solve the geometry problem and this “intuition” guides the symbolic AI component. AlphaGeometry was able to achieve results that are almost on par with what top, or gold medal winning, high school students competing in the annual international math competition score on the same sorts of problems.
The DeepMind researchers noted that many of the proofs AlphaGeometry developed were still not as elegant as those humans have developed, generally taking significantly more steps to solve a problem than the top humans do.
But, at the same time, they said that AlphaGeometry’s neural network component, in the process of its training, seems to have discovered some unusual approaches that may indicate geometric theorems previously unknown to mathematics. They said it would take further research to determine whether this, in fact, the case.
A lack of training data has been one of the issues that has made it difficult to teach deep learning AI software how to solve mathematical problems. But in this case, the DeepMind team got around the problem by taking geometry questions used in International Mathematics Olympiads and then synthetically generating 100 million similar, but not identical, examples. This large dataset was then used to train AlphaGeometry’s neural network. The success of this approach is yet another indication that synthetic data can be used to train neural networks in domains where a lack of data previously made it difficult to apply deep learning.