Called AlphaGeometry2, it can solve geometry problems better than maths masters.
AlphaGeometry2 is the artificial intelligence system created by DeepMind, Google’s leading AI research lab. According to its creators, it can solve geometry problems better than master mathematicians.
Winner of Maths Olympiad beaten by AI
AlphaGeometry2, an improved version of AlphaGeometry, was released by DeepMind in January last year. In a new study, the researchers claim their AI can solve 84 per cent of geometry problems from the last 25 years of the IMOs, a maths competition for high school students.
So why is DeepMind interested in a maths competition for high school students? The lab believes that the key to more powerful AI could lie in discovering new ways to solve difficult geometry problems, particularly those in Euclidean geometry.
Proving mathematical theorems requires both reasoning and the ability to choose from a range of possible steps towards a solution. These problem-solving skills may prove to be a useful component of future general-purpose AI models.
A hybrid system to solve complex problems
AlphaGeometry2 combines several key elements, including a language model from Google’s Gemini family and a ‘symbolic engine’. The Gemini model supports the symbolic engine, which uses mathematical rules to deduce solutions to specific problems, making it possible to obtain plausible proofs for a given geometric theorem.
In practice, AlphaGeometry2’s Gemini model suggests steps and constructions in a formal mathematical language to the engine, which checks their logical consistency according to specific rules. A search algorithm allows AlphaGeometry2 to search for solutions in parallel and store potentially useful results in a common knowledge base.
Out of a set of 50 problems selected from IMO competitions over the last 25 years, AlphaGeometry2 solved 42 of them, beating the average gold medallist score of 40.9. There are, however, some limitations. A technical feature prevents AlphaGeometry2 from solving problems with a variable number of points, non-linear equations and inequalities. In addition, the AI performed worse on a set of IMO harder problems, solving only 20 out of 29.
The future of AI debate
The results of the study are likely to fuel the debate about how AI systems should be built: through symbol manipulation or neural networks, which are considered more brain-like. AlphaGeometry2 takes a hybrid approach: its Gemini model has a neural network architecture, while its symbol engine is rule-based.
Proponents of neural network techniques claim that intelligent behaviour can only emerge from vast amounts of data and computing power. In contrast, proponents of symbolic AI argue that it may be better able to efficiently encode knowledge of the world, reason through complex scenarios and ‘explain‘ how it arrived at an answer.
