Will it be a golden age or a dark age for mathematics (and science)?

gist

In a guest post on Terence Tao's blog, Francesco Maggi sets out two futures for mathematics as language models get better at proofs. In the golden age, the tools empower new scientists and stay inside an open research culture. In the dark age, output rises while independent human understanding withers and knowledge concentrates in a few hands. Across eight points he argues that the outcome depends on choices, and he proposes publicly governed research models.

ideas

• Proofs without understanding are not enough. Maggi says long machine-written Lean proofs come with messy natural-language translations, and that without human understanding there is no human mathematics, so society will need more mathematicians.
• Capabilities call for study, not speculation. He treats model performance as a phenomenon to examine and asks which of the roughly 4000 problems in OpenAI's October 2026 release went unsolved, since that would show where models help.
• Mathematization is the bigger prize. Inventing the language that makes reality intelligible, as Newton, Riemann and Shannon did, is not theorem proving, and cheaper proofs could open more of the natural and social sciences to it.
• Credit and training are under strain. Maggi says mathematicians tell him that a strong result no longer proves a student's ability, that researchers now guard ideas they once shared, and that peer review still has to establish meaning.
• Private control of frontier models is risky. He warns that academics will depend on the same proprietary systems that companies use to compete with them, and urges universities, societies and funders to build shared model infrastructure.

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