The Rise of AlphaGeometry: A New Era of AI in Mathematics

Math Models are Coming!

1/28/20242 min read

a blackboard with a bunch of diagrams on it
a blackboard with a bunch of diagrams on it

The world of mathematics is about to be revolutionized, and it's all thanks to the latest breakthrough from Google DeepMind. AlphaGeometry, an AI system developed by Thang Luong and his team, is now capable of solving some of the most complex geometry problems from the International Mathematical Olympiad (IMO) with almost the same proficiency as the best human contestants. This development marks a significant milestone in the journey towards artificial general intelligence (AGI).

The IMO, a prestigious annual competition for secondary school students, is renowned for its challenging problems that require mathematical creativity. Until now, AI systems have struggled to demonstrate this level of creativity, with even specialized AIs failing to perform as well as average contestants. However, AlphaGeometry is changing the game.

The secret to AlphaGeometry's success lies in its unique approach to training. Instead of relying on the limited data available from past IMO competitions, Luong and his team created a tool that generates hundreds of millions of machine-readable geometrical proofs. This vast dataset allowed them to train AlphaGeometry to a level where it can now answer 25 out of 30 IMO geometry questions correctly, compared to an estimated score of 25.9 for an IMO gold medallist.

AlphaGeometry consists of two parts, each representing a different thinking system in the brain: a fast, intuitive system and a slower, more analytical one. The intuitive part, a language model called GPT-f, suggests theorems and arguments for a problem, while the symbolic reasoning engine constructs the argument using logical and mathematical rules. These two systems work in tandem, switching between one another until the problem is solved.

While AlphaGeometry's answers may not be as elegant as human proofs, they are undeniably effective. In fact, the AI even discovered a more general solution to a question from the 2004 IMO than the one listed in the official answers. This demonstrates the potential for AI to not only replicate human mathematical abilities but also to surpass them.

However, AlphaGeometry's current capabilities are still limited to the mathematics taught below undergraduate level, as per the IMO's requirements. Expanding its knowledge base could lead to even more impressive results, potentially even new mathematical discoveries. Additionally, it would be fascinating to see how AlphaGeometry handles not knowing what it needs to prove, as this is often where mathematical insight arises.

The implications of AlphaGeometry's success extend beyond the realm of mathematics. As Luong stated, "Our [current] AI systems are still struggling with the ability to do things like deep reasoning, where we need to plan ahead for many, many steps and also see the big picture." By demonstrating its ability to perform complex mathematical reasoning, AlphaGeometry brings us one step closer to achieving AGI.

With the $10 million AI Maths Models prize fund from XTX Markets, the race is on to develop an AI system that can win an IMO gold medal. AlphaGeometry's progress in solving IMO geometry problems is an exciting development in this competition, and it will be fascinating to see how this technology evolves in the coming years.

In conclusion, the rise of AlphaGeometry signals a new era of AI in mathematics. As professionals and businesses look to harness the power of AI, understanding and leveraging advancements like AlphaGeometry will be crucial for staying ahead in the rapidly evolving world of artificial intelligence.

https://www.newscientist.com/article/2412739-deepmind-ai-solves-hard-geometry-problems-from-mathematics-olympiad/