Terence Tao on What Mathematicians Really Value in the Age of AI
Mathematics in the Age of AI
In an essay based on his 2026 ICM lecture, Terence Tao sidesteps the debate over AI's capabilities and asks a deeper question: what are the true goals and values of mathematical research? Using problem-solving as a case study, he explores how the mathematical community might respond when AI can perform research-level tasks, offering a thought-provoking perspective on the future of the field.
Rather than debating the capabilities of such tools, we condition on the hypothesis that these capabilities will arrive, and examine instead a question that is orthogonal to it: what the goals and values of mathematical research actually are.
- sonicrocketman
Tao's Rule of Thumb (which applies very well to software):
> My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.
- highfrequency
Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument."
- itissid
What is being made is "what are our core values?" argument. One does not need to be a mathematician to know how poorly this worked for large communities when incentives are misaligned...
If a subset of mathematicians, use AI to condense timelines focusing on goal 6.2 exclusively and make rapid progress and reach a proverbial inflection point — one where value proposition of the using this new normal is too enticing to give up — everyone will ask: "This thing is so awesome. Why should I care about your values?"
- piker
If you're having dinner like me and prefer to watch: https://www.youtube.com/watch?v=M0--ZH1lOzg
- a2ff6eeb0
I don't know why anyone should care about understanding the results if the AI is better at math than us. It'd be like demanding that human mathematicians are banned from publishing until their cats understand the theorems.
If Amazon uses AI math to come up with better routing, the cats can benefit from cheaper delivery fees just as much as humans can. No understanding needed.
The human brain is being obsoleted, soon thinking is going to be a recreational activity like weightlifting. If you want to think as a hobby, that's fine, but most people will be free of that toil of unwanted brain labor.
- caglaroktay
AI also can replace a lot of expert attention too. Why not? What is useful or what is not useful is based on the expert's narrow opinion. An AI system can do much more and deep value comparison. It looks like if our current technological advancement continues, in the space of what is possible (or even impossible), AI can find the optimal solutions better than any human or human organizations. But I think there is only one think will remain for humans to go for these solutions: what we value. that will be the last resort I believe and hopefully ai systems won't start manipulate us too as we are very fragile on manipulation.
- sonicrocketman
Anyone else print their white papers before reading? (At least the short ones)
- glimshe
Terence Tao sees a role for AI in science. I'm no genius but he basically described what I've thought all along... We don't need to be "all in" or "all out".
It's the old cliche of "if you only have a hammer every problem looks like a nail". Let's not fall into the trap of thinking that our life needs to be 100% about AI or completely devoid of AI. We can really use this thing to make our lives better.
Instead of wasting time on the question of whether we should use it, let's focus on HOW we'll use it.
And one thing about Tao: it's really refreshing to have an influential genius "around" who isn't a egomaniacal psychopath trying to rule the world through their XYZ corporation but, instead, being a reasonable and well-balanced person. Big fan.