discovery-acceleration
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Will it be a golden age or a dark age for mathematics (and science)?
opinion
17 min read
Francesco Maggi argues that large language models could accelerate mathematical and scientific discovery but could also concentrate knowledge and weaken independent human research. He cites LLM-generated work including a finite-time blow-up solution for the forced Navier–Stokes equations and a proposed proof of the quasi-Riemann Hypothesis, while stressing that mathematicians must independently scrutinize, interpret, and assimilate such results. Lean, a proof assistant, can formally verify proofs, but important machine-generated Lean proofs may run to hundreds of thousands of lines and remain difficult to translate into understandable natural language. Maggi says theorem proving alone does not define mathematical progress: mathematicians also create new concepts and formal languages through “mathematization,” as exemplified by Newton, Riemann, Einstein, Shannon, and Grothendieck. He argues that authorship, citation, peer review, confidentiality, and the evaluation and training of researchers require new standards when LLMs contribute to research. He also warns that proprietary frontier systems could give a few companies disproportionate control over scientific priorities and capabilities. Maggi calls for coordinated, publicly governed scientific LLM infrastructure, researcher access to frontier systems, disclosure and reproducibility standards for LLM-generated scholarship, confidentiality protections, and research into effects on education and training. He argues these measures could preserve an open, intellectually independent scientific culture while using LLMs to support theory-building across mathematics and other sciences.