Tao Zhexuan comments on Google AlphaProof: AI shows 'extraordinary wisdom' in mathematics competitions

In the face of Mathematical Olympiad problems, the "IQ" of AI is often not enough. However, this is a thing of the past. Google DeepMind used AI to solve the real questions of this year's International Mathematical Olympiad IMO, and it was just one step away from winning the gold medal. For AI, Mathematical Olympiad is no longer a problem. Each of the six questions in IMO 2024 is worth 7 points, giving a maximum total score of 42 points. DeepMind's system ended up with a score of 28, meaning it received perfect scores for all four of the problems it solved - equivalent to the top score in the silver medal category.

2. Tao Zhexuan, a mathematician who commonly uses AI-assisted proofs, recently I am busy on a business trip and have not fully digested the problem solving engines AlphaProof and AlphaGeometry2. But he expressed his views on DeepMind’s AI system participating in the IMO competition on his blog.

   

   Tao Zhexuan talks about
3. This is a very great work that once again changes our expectations for AI-assisted or fully autonomous methods to achieve benchmark challenges.
4. For example, IMO-level geometry problems have been basically solved for dedicated AI tools, and IMO problems with formal proofs can be overcome by AI at least to some extent through reinforcement learning processes, although each problem currently requires considerable Computational quantities and require human help in formalization.
5. Tao Zhexuan believes that this method can also automate formal mathematics, which may promote mathematical research methods that include formal components. The resulting database of formal proofs could be a useful resource if it were shared more openly.
6. This approach (based on reinforcement learning, similar to the spirit of AlphaGo, with an emphasis on a holistic approach) is very clever and makes sense in hindsight. As the "AI Effect" goes, once explained, it doesn't feel like a display of human intelligence; but it is still an expansion of the capabilities of our AI-assisted problem-solving toolset.

   

   "AI Effect"

"AI Effect" means that when artificial intelligence technology makes progress or solves problems, people tend to think that these achievements are not real artificial intelligence or do not possess real intelligence. In other words, once a technology is understood or popularized, it is no longer considered intelligent. This phenomenon shows that people’s definitions and expectations of “intelligence” will continue to improve as technology advances.

NuminaMath Model

At the beginning of this month, Tao Zhexuan announced on his blog that the preliminary results of the AI ​​Mathematics Olympiad (AIMO Progress Award) have been announced. Among them, Numina’s team won first place.

The NuminaMath model is fully automated and orders of magnitude more resource efficient, and takes a completely different approach (using large language models to generate Python code to brute force solve regional competition-level numerical answer problems). This model is also completely open source.

DeepMind’s mathematical reasoning research

DeepMind also makes unremitting efforts in mathematical reasoning. At the beginning of this year, its artificial intelligence algorithm achieved a major breakthrough in the Mathematics Olympiad (IMO). The paper "Solving olympiad geometry without human demonstrations" introduced AlphaGeometry to the world, and was also published in the international authoritative journal "Nature". Experts say this is an important step towards artificial intelligence becoming capable of human reasoning.

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