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On October 28, 2026, Fields Medalist Laurent Lafforgue proposed in a lecture at Fudan University's "Pujiang Science Masters Forum" that without mathematicians' research and verification, AI-generated mathematical texts lose their meaning. He pointed out that large language models can predict tokens and complete texts, implying that some as-yet-unidentified mathematical structure exists within the human text corpus, but engineers do not understand the essence of its success. Lafforgue drew on Grothendieck's topos theory, arguing for treating all texts as a whole space and using the language of "sheaves" and "coverings" to approximate this structure. He emphasized that AI operates entirely within the space of human language and cannot see things that have not yet been named, and that mathematicians' research and verification are irreplaceable. This view was currently reported by The Paper on October 30.
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The Paper
Fields Medalist Lafforgue: Without mathematicians' research and verification, AI-generated mathematical texts lose their meaning
In a speech at Fudan University's "Pujiang Science Masters Forum," Fields Medalist Laurent Lafforgue pointed out that large language models can predict tokens and complete texts, suggesting that some as-yet-unidentified mathematical structure exists within the corpus of human texts, but engineers do not understand the essence of its success. Drawing on Grothendieck's topos theory, he advocated treating all texts as a whole space and approximating this structure with the language of "sheaves" and "coverings." He emphasized that AI operates entirely within the space of human language and cannot see things that have not yet been named, and that mathematicians' research and verification are irreplaceable.
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