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Can AI do maths yet? Thoughts from a mathematician.

Dec 23, 2024 - xenaproject.wordpress.com
The article discusses the recent performance of OpenAI's new language model, o3, which scored 25% on the FrontierMath dataset—a secretive collection of challenging math problems curated by Epoch AI. FrontierMath consists of "find this number!" questions with definitive, computable answers, designed to be difficult even for research mathematicians. The dataset's secrecy is intended to prevent language models from training on it and simply recalling answers. The author, an academic mathematician, expresses surprise at o3's performance, as they believed AI was still at an undergraduate level in mathematics. However, a claim that 25% of the problems are undergraduate-level tempers this surprise, and the author anticipates further AI advancements in solving more complex problems.

The article also highlights the distinction between solving numerical problems and proving theorems, with the latter being more relevant to research mathematics. While AI has made strides in solving high school-level problems, such as those in the International Mathematics Olympiad (IMO), it still struggles with logical reasoning and providing human-understandable explanations for proofs. The author emphasizes the need for AI to advance beyond merely finding numbers to proving theorems correctly and comprehensibly. Despite rapid progress, the author believes AI is still far from surpassing the "undergraduate barrier" in mathematics.

Key takeaways:

  • OpenAI's new language model, o3, achieved a 25% score on the challenging FrontierMath dataset, which consists of hard math questions with definitive, computable answers.
  • The FrontierMath dataset is secretive to prevent language models from training on it, and its problems are considered extremely challenging, often requiring advanced mathematical knowledge.
  • There is skepticism about the level of difficulty of the problems in the dataset, with some suggesting that a portion of them are undergraduate-level, which may explain o3's performance.
  • While AI is progressing rapidly in solving mathematical problems, there is still a significant gap in its ability to generate original proofs and explanations that are comprehensible to humans.
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