AI-assisted math advance highlights gap between finding answers and judging their significance
AI models are good at finding answers to mathematical puzzles but are not as good at research judgment, according to theoretical computer scientists.
The use of artificial intelligence in mathematical research has highlighted the gap between finding solutions and judging their significance, according to theoretical computer scientists. Princeton's Pravesh Kothari and his co-leads used AI to make progress on the Grothendieck constant, a problem first identified by Alexander Grothendieck in 1953.
AI models excel at finding answers because they are trained on published papers, textbooks, and solved problems. However, they fall short when it comes to recognizing the value of a theoretical result, determining its significance, and assessing its downstream use. This is because the training data rarely includes information on the long process of mathematical discovery, which involves failed approaches, unlikely results, and changes in strategy.
The researchers successfully narrowed the bounds of the Grothendieck constant using AI tools, but the results are not yet peer-reviewed. The work has implications for creating more efficient algorithms in graph theory and quantum information. Kothari noted that AI models did most of the work, with humans providing guidance only when the models got stuck.
Mathematicians are increasingly using AI, with recent highlights including OpenAI disproving Paul Erdős's 1946 unit-distance conjecture and solving the Navier-Stokes problem. However, there is disagreement among mathematicians about the impact of AI on the field. Some argue that AI outpaces humans at finding answers, while others believe that AI solutions can't replace the community process of mathematical discovery.
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