Google's AI has just shown it can do more than recommend cat videos or predict your next text – it's now flexing its math muscles on an international stage. In an unexpected twist, Google's AI systems, AlphaProof and AlphaGeometry 2, have achieved a silver medal-level performance at the International Mathematical Olympiad (IMO), one of the toughest math competitions in the world.

What is AlphaProof?

AlphaProof is a new AI system from Google. It doesn’t just do basic arithmetic; it dives into the complex world of formal mathematical reasoning. Using a combination of language models and the AlphaZero reinforcement learning algorithm (the same one that mastered chess and Go), AlphaProof trains itself to solve math problems in a formal language called Lean. Think of it as learning a new language but for math geniuses.

At the IMO, AlphaProof tackled two tough algebra problems and a number theory problem. It even solved the hardest problem of the competition, something only five human contestants managed to do. This achievement makes AlphaProof look like the Einstein of AI, showing it can handle some of the most challenging math puzzles out there.

What is AlphaGeometry 2?

AlphaGeometry 2 is an improved version of Google’s previous geometry-solving AI. It uses a neuro-symbolic hybrid approach, combining a sophisticated language model with a powerful symbolic engine. This upgrade enabled AlphaGeometry 2 to solve complex geometry problems more efficiently.

In the IMO, AlphaGeometry 2 tackled Problem 4 in just 19 seconds. This problem involved intricate geometric constructions and required a deep understanding of angles, ratios, and distances. The system was trained on a much larger dataset than its predecessor, which helped it solve 83 percent of historical IMO geometry problems from the past 25 years. This training ensured that AlphaGeometry 2 could handle the most challenging geometry problems presented in the competition.

Impressive Performance at the IMO

The IMO is no easy feat. Every year, the best young mathematicians from around the world spend countless hours training to solve incredibly difficult problems in algebra, combinatorics, geometry, and number theory. Google's AI systems scored 28 out of 42 points, earning them a spot in the silver medal category. They were just one point shy of a gold medal – talk about a close call!

Esteemed mathematicians, including Fields Medal winner Prof Sir Timothy Gowers and IMO 2024 Problem Selection Committee Chair Dr. Joseph Myers, evaluated the AI's solutions. Their verdict? Google’s AI can come up with some seriously impressive and non-obvious solutions, showing it’s got the right stuff to compete with the best.

Google’s success with AlphaProof and AlphaGeometry 2 marks a significant advancement in AI’s ability to perform complex mathematical reasoning. This breakthrough could transform various fields by enabling mathematicians to explore new hypotheses, solve longstanding problems, and automate time-consuming parts of mathematical proofs.

Looking ahead, Google plans to release more technical details about AlphaProof and continue exploring different AI approaches to enhance mathematical reasoning. The goal is to create AI systems that can work alongside human mathematicians, pushing the boundaries of what is possible in science and technology.

Boston Institute of Analytics, IndiaAI