Gowers opens with a childhood episode about attempting Fermat’s Last Theorem and discovering difference sequences, using it to illustrate the deep learning that comes from struggling with problems. He explains his refusal to sign a letter by 25 Fields medallists because he disagrees with its apparent claim that conceptual understanding should be prioritized over problem-solving. He frames mathematics as a spectrum between problem-solvers and concept-seekers and warns that casting one temperament as “right” risks alienating large parts of the community. He also stresses his independence from OpenAI (contacts and early access but no payment) and notes that his work on automated theorem proving makes the rapid rise of LLMs a painful pivot rather than a simple endorsement. He cites analogous commentary by Jacob Tsimerman, Daniel Litt, and Noah Smith as consonant with his view.
He contrasts two concrete futures. In one, powerful models are public and solve many problems faster than humans, producing floods of correct results that the community cannot absorb; many solutions require near-zero human effort. In the other, release is restricted and industry mathematicians defer solving major problems until a representative community body approves. For individual understanding, models increase available results and provide help when stuck, but they also threaten the mental discipline built by long, hard problem-solving - an effect likened to overreliance on satnav. He offers this nuanced analysis to argue that the crisis is real but complex, with trade-offs that deserve careful thought rather than a single prescriptive stance.
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