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On October 31, 2026, Laurent Lafforgue, winner of the 2002 Fields Medal and a senior expert at Huawei France, proposed in a speech at the 2026 World Laureates Forum that there may exist behind large language models an as-yet-unidentified "text space" whose intrinsic structure needs to be described mathematically. Drawing on Grothendieck's line of thinking, he argued that the model is not attaching a unique meaning label to each sentence, but rather observing, within a vast text space, which continuation paths are viable and with what probability. Reports from the same day also noted that Lafforgue pointed out that large language models can already solve some mathematical problems, even touching on problems that human mathematicians had not solved in the past, and that the way mathematics doctoral students are trained is bound to change; however, he does not regard AI as a replacement for mathematicians, believing that humans can still pose new questions and create new concepts.
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Nov 1
Shanghai Observer
2026 World Laureates Forum Opens: Nobel and Fields Medalists Discuss How AI Is Changing the Scientific Research Paradigm
The 2026 World Laureates Forum opened in Shanghai on October 31, under the theme "Paradigm Shift: The Next Decade of Scientific Breakthroughs." Omar Yaghi, winner of the 2025 Nobel Prize in Chemistry, proposed developing "selection science"; his team used large models to generate 96 sets of candidate crystallization conditions, which were then verified by a robotic platform, and within less than a month the crystallization performance of the material improved significantly. Laurent Lafforgue, winner of the 2002 Fields Medal, in turn asked where mathematicians' creativity lies once machines excel at proof.
Oct 31
Shanghai Observer
Fields Medalist Laforgue: Mathematicians should describe the "text space" behind large language models
Laurent Laforgue, winner of the 2002 Fields Medal and a senior expert at Huawei France, proposed at the 2026 World Laureates Forum that there may exist behind large language models a not-yet-identified "text space" whose internal structure needs to be described mathematically. Drawing on Grothendieck's line of thinking, he argues that the model is not attaching a unique meaning label to each sentence, but rather observing, within a vast text space, which continuation paths are viable and with what probability. He does not regard AI as a replacement for mathematicians, and conjectures that mathematical writing may return to a more traditional style.
Shanghai Observer
Fields Medalist Laforgue: AI is getting better and better at generating, and more "human mathematics" is needed
Laurent Laforgue, winner of the 2002 Fields Medal and a senior expert at Huawei France, pointed out in his speech at the 2026 World Laureates Forum that large language models can already solve some mathematical problems, even involving problems that human mathematicians had not solved in the past, and that the way mathematics doctoral students are trained is bound to change. He believes that AI can handle a large amount of existing knowledge and text, but humans can still raise new questions and create new concepts, and that "we can use AI, but we can do more than AI."