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Mathematics in the age of AI

Terence Tao · 17 Aug 2026 · arxiv.org

5 korrents from this paper

In plain words

If AI can do research math, the community must make explicit what it really values, because chasing solutions alone will no longer serve the rest of the enterprise. Without that, correct proofs will pile up faster than anyone can understand, accept, or fold into the standard theory, and systems built for scarce proofs will strain under abundance. It is an essay arguing a position that assumes AI capability is coming and uses problem solving as a case study to unpack what the field actually optimizes for once those goals stop lining up.

Our summary of the paper, not the authors' words — written to be readable without the field's vocabulary, from the stored copy of the paper and nothing else. Drafted with xai:grok-4.5 and checked by a person. The authors' own sentences are the quotes below.

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Every claim below was made in this piece, quoted word for word and numbered in the order the piece makes them, so you can read it there rather than take our word for it. The sentence above each quote is our reading of the claim, not their wording. Each quote was checked against a stored copy of the page at build time; where the two differ, the quote is the fact.

  1. I believe that we are now entering a era of comparable turbulence in mathematics. This time, though, what is being stress-tested is not our foundational framework for mathematical truth, but rather the largely implicit framework of mathematical values and practices: what we consider a contribution to be, what we reward, what we regard as understood, and who - or what - we regard as having done the work.
  2. I argue that it will become necessary to make these unwritten goals of mathematics much more explicit; but once we have thoroughly examined and codified them, our community will emerge stronger and more resilient than before.
  3. Consequently, excessive optimization for one or two goals may cause the many previously aligned goals of mathematics to diverge from one another;
  4. An excessively AI-polished proof may sand away both the "artificial" friction (typos, awkward phrasing, disorganization) and the "natural" friction, leaving a text that is easy to read and hard to learn from.
  5. But passing an automatic filter is not a substitute for community acceptance; I do not believe that human referees can be removed from the publication process.