Google claims math breakthrough with proof-solving AI models

🌈 Abstract

The article discusses the recent announcement by Google DeepMind that their AI systems, AlphaProof and AlphaGeometry 2, have achieved a silver medal-level performance in the International Mathematical Olympiad (IMO), a prestigious math competition. The article explores the capabilities of these AI systems, their limitations, and the broader implications for the future of mathematical research.

🙋 Q&A

[01] Google DeepMind's AI Systems and the IMO

1. What are the key achievements of Google DeepMind's AI systems in the IMO?

• AlphaProof and AlphaGeometry 2 reportedly solved 4 out of 6 problems from the 2023 IMO, achieving a score equivalent to a silver medal
• AlphaProof uses reinforcement learning to prove mathematical statements in the formal language called Lean, while AlphaGeometry 2 is an upgraded version of Google's previous geometry-solving AI model
• The combined system earned 28 out of 42 possible points, just shy of the 29-point gold medal threshold, and achieved a perfect score on the competition's hardest problem

2. What are the limitations and qualifications mentioned regarding the AI systems' performance?

• The AI systems took significantly longer than human competitors to solve the problems, with some taking up to 3 days
• The problems were first translated into formal mathematical language for the AI to process, while human contestants work directly with the problem statements
• The "autoformalization" step was done by humans, and the AI performed the core mathematical reasoning

3. What are the broader implications for mathematical research discussed in the article?

• There is uncertainty about whether mathematicians will become redundant, with the article suggesting that a breakthrough or two is still needed for the AI systems to "solve mathematics"
• However, the article suggests that such AI systems could become valuable research tools, enabling mathematicians to get answers to a wide range of questions, provided they are not too difficult

[02] Perspectives from Mathematicians

1. What is Sir Timothy Gowers' perspective on the achievements of the Google DeepMind AI systems?

• Gowers acknowledges the achievement as "well beyond what automatic theorem provers could do before"
• However, he points out that the AI systems took much longer than human competitors to solve the problems, and had much faster processing speed than the "poor old human brain"
• Gowers also notes that the problems were first translated into formal language by humans before the AI systems could work on them

2. How does Gowers view the broader implications for mathematical research?

• Gowers expresses uncertainty about whether mathematicians are becoming redundant, suggesting that a breakthrough or two is still needed for the AI systems to "solve mathematics"
• However, Gowers speculates that such AI systems could become valuable research tools, enabling mathematicians to get answers to a wide range of questions, provided they are not too difficult