Fields Medalist Terence Tao warns AI could produce more math proofs than humans can handle
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Tao, 51, an Australian and American mathematician recognized for his contributions to partial differential equations, combinatorics, harmonic analysis, and additive number theory, made the remarks in his lecture, "Mathematics in the Age of AI," delivered at the International Congress of Mathematicians (ICM) last weekend. His speech drew widespread attention from the global mathematics community. He began by reflecting on mathematics between 1900 and 1930, when breakthroughs such as Russell's paradox (1901) and the Gödel incompleteness theorems (1931) forced mathematicians to reexamine the discipline's underlying assumptions. He said this "was a turbulent period for mathematics, but the end product was extremely valuable: an explicit, rigorous, and standardized foundational framework." Noting that there is scope for further improvement, he stated: "I believe we are entering a similarly turbulent period, a crisis in the foundations of mathematical values and practices." Tao cited his First Proof experiment, conducted in May, in which frontier AI models successfully solved seven out of 10 novel research-level mathematics problems under controlled scientific conditions. The results were refereed by experts for both correctness and exposition, with the resulting proofs considered to be of publishable quality. Based on those results, he developed a "Working Hypothesis" predicting that "AI tools will, reasonably soon, become capable of performing a reasonable fraction of research-level mathematical tasks, with reasonable levels of success, quality, supervision, and cost." Assuming the Working Hypothesis holds, he argued that the central question will shift from what AI is capable of to: "What are the precise goals, objectives, and values of our mathematical community, and the enterprise of mathematical research?" Traditionally, those goals have included solving unsolved pure and applied problems, developing new theories and techniques, and understanding the world. Additional goals involve building a community of mathematicians, training the next generation to guide future directions, contributing to a shared network of mathematical knowledge, and creating enduring works of aesthetic value. In the past, these goals have been largely positively correlated, with progress in one typically leading to progress in the others, Tao explained. However, he warned that "all m…
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外部发现 · 陶哲轩 · Original source ↗ · Site entry ·