Terence Tao
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Their wordsMost of the value that flows into the world from mathematics and the work of mathematicians will not be replaced by AI, but could be magnified.
↗A value-based approach to mathematicsterrytao.wordpress.com 1st of 3 in this piece
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mathematicsAI and human skilleducation
Their wordsImproper usage of AI offloads thinking, understanding and learning, thus mortgaging future mathematical development.
↗A value-based approach to mathematicsterrytao.wordpress.com 2nd of 3 in this piece
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Their wordsThe value of math, like so many other forms of knowledge, also comes from the process, not just the product.
↗A value-based approach to mathematicsterrytao.wordpress.com 3rd of 3 in this piece
- 6 weeks earlier
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Their wordsI 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.
↗Mathematics in the age of AIarxiv.org All 5 from this paper
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Their wordsI 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.
↗Mathematics in the age of AIarxiv.org All 5 from this paper
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Their wordsConsequently, excessive optimization for one or two goals may cause the many previously aligned goals of mathematics to diverge from one another;
↗Mathematics in the age of AIarxiv.org All 5 from this paper
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Their wordsAn 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.
↗Mathematics in the age of AIarxiv.org All 5 from this paper
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Their wordsBut 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.
↗Mathematics in the age of AIarxiv.org All 5 from this paper
- 6 weeks earlier
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Their wordsWe argue that the next leap in AI4Math systems requires a decisive shift from predefined problem-solvers to research agents that can address frontier mathematical challenges with rigorous formal mathematical reasoning.
↗From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier (with 18 co-authors)arxiv.org All 4 from this paper
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Their wordsHowever, these LLM reasoners that generate informal reasoning in natural language are fundamentally limited by the lack of precise, machine-checkable semantics, making their outputs prone to hallucinations [Huang et al., 2025b] and precluding autonomous verification, a prerequisite for tackling open-ended mathematical research.
↗From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier (with 18 co-authors)arxiv.org All 4 from this paper
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Their wordsDespite these strides, we argue that current AI4Math systems still largely operate as solvers, excelling at isolated, well-defined proof generation rather than as researchers capable of expanding the boundaries of mathematical knowledge.
↗From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier (with 18 co-authors)arxiv.org All 4 from this paper
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Their wordsThese developments inform our position that AI systems are now capable of meaningful contributions to formal mathematics, not merely informal problem-solving.
↗From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier (with 18 co-authors)arxiv.org All 4 from this paper
- 4 months earlier
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Their wordsSo, I think AI has basically driven the cost of idea generation down to almost zero in a very similar way to how the internet drove the cost of communication down to almost zero, which is an amazing thing, but it you know, it it it doesn't make it doesn't create abundance by itself.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 1st of 24 in this recording
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Their wordsSo, we're now in a situation where suddenly people can generate thousands of theories for a given scientific problem. And now we have to to verify them, evaluate them and this is something which we we have to to change our structures of science to actually sort this out.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 2nd of 24 in this recording
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reinforcement learningmetascience
Their wordsSo, you you can't look at any given scientific achievement purely in isolation and give it an objective grade without being aware of the context both in the the past and the future. And so it it it may never be something that you can just reinforcement learn the same way that that you can for much sort of more localized problems.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 3rd of 24 in this recording
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Their wordsyou know, right now we're going through uh an in um an cognitive version of the Copernican revolution where we used to think that human intelligence is the center of the universe. And now we're actually seeing that there's there's very different types of intelligence um that that that are out there uh with very different strengths and weaknesses.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 4th of 24 in this recording
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Their wordsUm we are seeing a lot fewer sort of pure AI solutions now where um they are just one shots the problem. Um so so there was there was a month where that happened and and that has stopped.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 5th of 24 in this recording
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Their wordsum you know, these tools they either succeed or they fail um and they they've been really bad at creating sort of partial progress or identifying intermediate um um stages that you should you should focus on first.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 6th of 24 in this recording
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Their wordsYeah, so they excel at breadth and humans excel at depth. Um like human experts at least. Yeah, so um I think they're very complementary. Um but our current uh way of doing math and science is focused on depth because that that's where the human uh expertise cuz humans can't do breadth.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 7th of 24 in this recording
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Their wordsSo, I think AI-type tools we really will will actually revolutionize the ex- the experimental side of math where where um you don't care so much about uh individual problems and and the process of solving them, but you you want to gather just large-scale data about about what things work, what things don't.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 8th of 24 in this recording
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Their wordsSo, they they they still make mistakes, but but um um I've I've tested these tools, you know, on on on on um like little tasks that I can do and and sometimes they pick up errors I make, sometimes I pick up errors that they make. It's it's about a tie right now.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 9th of 24 in this recording
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Their wordsUm and then they can kind of suggest random things and it it but it it it um often I find that trying to chase them down and make them work and find they don't work, it wastes more time than it saves.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 10th of 24 in this recording
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Their wordsUm So, like with the Erdős problems, you know, like almost all of the 50 problems that were solved by AIs were ones for which basically there was no literature.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 11th of 24 in this recording
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Their wordsUh but whenever we do a systematic study, um any given problem, an AI tool has a success rate of maybe 1 or 2%. Uh it's just that it's just that they can apply at scale and and you just pick the winners, it looks great.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 12th of 24 in this recording
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Their wordsUm so yeah, the the the um the core of what I do, like actually solving um the most difficult part of of a math problem, that hasn't changed too much. I still use pen and paper for that.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 13th of 24 in this recording
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Their wordsUh yeah, so it's it's made papers sort of richer and broader, but not necessarily deeper.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 14th of 24 in this recording
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Their wordsThere isn't this cumulative process which is, uh, sort of built up interactively. Um, it it it seems to be a lot more trial and error and just repetition, brute force, um, you know, which can see it scales and it can work amazingly well in in certain contexts, um, but yeah, this this idea this this sort of building up cumulatively from, um, from partial progress is kind of is what's still not quite there yet.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 15th of 24 in this recording
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Their wordsYeah, you you you're on a new session it's forgotten what what it just did. Um, it it has you know, it has no new skills to to attach to to to build on on on related problems.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 16th of 24 in this recording
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Their wordsI mean, some problems have been basically solved by pure brute force. The four color theorem is is a famous example. Um, we have still not found a conceptually elegant proof of this theorem.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 17th of 24 in this recording
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Their wordsI I I I do feel that, you know, fully autonomous one-shot approaches are not the right approach for these problems. I mean, I I think you you'll get a lot more mileage out of the interplay between between humans collaborating with these tools.
↗Terence Tao – How the world’s top mathematician uses AIyoutube.com 18th of 24 in this recording