08-31-2026, 07:30 PM
Care for a little more AI?
Author: Hugo Duminil-Copin
Published: August 30, 2026
Fields Medalist Hugo Duminil-Copin argues that although the recent progress of AI in mathematics is extraordinary—and frontier models already surpass individual mathematicians at many tasks—the rapid use of AI to attack major open problems may damage something essential about mathematical research. His central example is the percolation-theory conjecture $\theta(p_c)=0$. Duminil-Copin spent years thinking about this problem without solving it, yet those unsuccessful attempts led to collaborations, new techniques, and results in other areas. For him, an open problem is therefore not merely a statement waiting for a proof: it acts as a “lighthouse” that guides exploration and generates ideas. If AI rapidly eliminates such problems, it may remove the intellectual environments in which new mathematical understanding develops.
His deeper concern is that mathematics could become too focused on producing theorems rather than producing understanding. Mathematical intuition develops slowly through failed attempts, experimentation, discussion, and years of engagement with ideas. Duminil-Copin worries that AI-generated solutions could compress this process so dramatically that young mathematicians lose important opportunities to develop creativity and mathematical judgment. He describes current AI use as potentially “petrifying” rather than empowering mathematicians: fields could have their central conjectures solved before the surrounding ideas and methods have matured. This raises difficult questions for PhD students in particular—what long-term problem should someone devote years to if an AI system might solve it suddenly?
Duminil-Copin does not argue that AI should never be used in mathematics. He acknowledges that areas with important scientific applications may benefit enormously from accelerated discovery, and he does not propose a universal rule restricting AI. Instead, he rejects a purely utilitarian conception of mathematics in which faster theorem production is automatically considered progress. Mathematics, in his view, is also a human intellectual adventure: learning to search, doubt, experiment, fail, restart, and eventually understand. For his own research, he has therefore chosen not to use AI as a replacement for the creative mathematical process.
Key takeaways
ARTICLE
Author: Hugo Duminil-Copin
Published: August 30, 2026
Fields Medalist Hugo Duminil-Copin argues that although the recent progress of AI in mathematics is extraordinary—and frontier models already surpass individual mathematicians at many tasks—the rapid use of AI to attack major open problems may damage something essential about mathematical research. His central example is the percolation-theory conjecture $\theta(p_c)=0$. Duminil-Copin spent years thinking about this problem without solving it, yet those unsuccessful attempts led to collaborations, new techniques, and results in other areas. For him, an open problem is therefore not merely a statement waiting for a proof: it acts as a “lighthouse” that guides exploration and generates ideas. If AI rapidly eliminates such problems, it may remove the intellectual environments in which new mathematical understanding develops.
His deeper concern is that mathematics could become too focused on producing theorems rather than producing understanding. Mathematical intuition develops slowly through failed attempts, experimentation, discussion, and years of engagement with ideas. Duminil-Copin worries that AI-generated solutions could compress this process so dramatically that young mathematicians lose important opportunities to develop creativity and mathematical judgment. He describes current AI use as potentially “petrifying” rather than empowering mathematicians: fields could have their central conjectures solved before the surrounding ideas and methods have matured. This raises difficult questions for PhD students in particular—what long-term problem should someone devote years to if an AI system might solve it suddenly?
Duminil-Copin does not argue that AI should never be used in mathematics. He acknowledges that areas with important scientific applications may benefit enormously from accelerated discovery, and he does not propose a universal rule restricting AI. Instead, he rejects a purely utilitarian conception of mathematics in which faster theorem production is automatically considered progress. Mathematics, in his view, is also a human intellectual adventure: learning to search, doubt, experiment, fail, restart, and eventually understand. For his own research, he has therefore chosen not to use AI as a replacement for the creative mathematical process.
Key takeaways
- Open problems have value beyond their solutions. Failed attempts can create techniques, collaborations, intuitions, and entirely new research directions.
- The real goal of mathematics is understanding, not theorem production alone. AI may optimize the latter while unintentionally weakening the former.
- Young researchers may be especially affected. Rapid AI solution of conjectures could destabilize the traditional way mathematicians choose and develop long-term research programs.
- Duminil-Copin's position is not simply anti-AI. His argument is that mathematics should carefully distinguish areas where AI acceleration is valuable from areas where the slow human process of discovery is itself a major part of the value.
ARTICLE
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