Fields Medalist Yu Deng on Hilbert's 6th Problem, Randomness, and AI in Mathematics

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Yu Deng, a 2026 Fields Medal recipient, gave an in-depth interview discussing his breakthrough work on Hilbert's sixth problem, which had remained unsolved for over 125 years. His research builds a rigorous mathematical bridge between microscopic particle systems governed by Newtonian mechanics and macroscopic fluid dynamics equations. Deng explained that randomness, rather than complicating such problems, often simplifies them by allowing researchers to focus on typical outcomes instead of tracking every individual particle trajectory. He also shared that AI tools are becoming valuable collaborators in mathematical research, recounting how GPT produced a one-page proof in an hour for a lemma that took him five days to prove across four pages. Looking ahead, Deng identified quantum field theory and the construction of infinite-dimensional measures, including the Yang-Mills problem, as among the most important open challenges he hopes to tackle next.

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