# Google claims math breakthrough with proof-solving AI models

## ๐ 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.

## ๐ 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