Why I Didn't Sign the Fields Medallists' Letter

This is really a microcosm of one particular problem that AI presents to the world: what do people do when their labour is not required any longer?

Here the worry is the social structures of mathematics are eroded such that fewer humans become able to do the work and less well, similarly to how juniors are being recruited less in software engineering, breaking the ladder and leading to fewer seniors in the years to come.

The answer to this really depends strongly on what AI can actually accomplish, but I’ll assume the maximal case and say that AI can do everything economically necessary, and further even those things just desired, such that human labour isn’t required for anything that anyone wants in a practical sense.

Here, we don’t need a human understanding of mathematics to give people a perfect standard of living. We also don’t need humans involved with anything else.

Everything therefore becomes a hobby or a game. People do things because they enjoy them for their own sake, or because they are endeavours used as vehicles to socialise and enjoy others’ company, or because a shared social belief exists and is cultivated such that doing such and such a thing confers social status.

And I think that’s more or less it. I predict we may see some fairly strange sorts of things, such as games where the team structure looks like the descendant of a company org and they compete in an artificial economy. Likewise we may see gamified versions of universities and academia. All of th […]

It has been a long time since I saw my WordPress theme in the wild. I had no idea wordpress.com still had it as an option.

edit: Link changed; it was https://terrytao.wordpress.com/2026/09/17/why-i-didnt-sign-t....

I thought one of the implicit points of the open letter was that unsolved problems are not something that falls out of the sky, they are a curated resource that people have spent time on and shared for the benefit of like-minded peers and humanity as a whole. And the AI companies treat them like they treat absolutely everything else: natural resources, literature, art, code etc. as something to be chucked into the ravening maw and pooped out the back as profit. They don't care if mathematics advances, they don't care if they strip-mine the available problems and damage the field. In fact, as with programming I think they see that as in their long-term interest - soon there will be no intelligence or creativity but the one that Sam Altman bills you for.

> In short, it seems to me that while a flood of “big” AI results would be likely to increase the amount of important mathematics that was not properly digested, it would also be likely to increase the amount that was properly digested, which seems like a pretty good bargain.

This seems like the crux of the argument to me, and I agree.

> my worry is not that we would be unable to [digest the mathematical results from the AIs], but rather that the social structures that currently support this digestion process will be destroyed and not adequately replaced.

A valid concern! And one we will all face soon enough, as AI continues to automate parts of jobs that were once manual.

I cook because I like to tinker, understand how variation in recipes affect flavor, and occasionally stumble upon something novel and tasty. The journey is most important but the goal is nice.

My wife cooks to produce a meal and feed our family. The journey is a necessary evil to achieve a goal.

We are aware of this difference in style and have learned to appreciate what each has to offer. At the same time, we sometimes annoy each other in the kitchen.

There is an analogy here to what this essay says.

> With that interpretation, the issue becomes slightly different: is it more important that the collective understanding of the mathematical community should be as advanced as possible or that there should be answers to as many problems as possible? Or are those two aims valuable in different ways, so that there is no point in declaring one of them more important? Or are they so inextricably linked that it makes no sense to argue that one is more important than the other? And when we say “important”, for whom are we saying it is important: for mathematicians, or for society as a whole?

This is easy to me. Truth should be the North Star. If there is a fundamental truth that can be found via mathematics, then the shortest route to that truth should be preferred. While LLMs are definitely capable of solving problems in search of truth, I agree with Tao that instant "true/false" results threaten to short-circuit the traditional avenues we have used to escape local minima in the search for truth. Their products may be the junk food that provides immediate satiation in exchange for long-term health. Perhaps it's wrong, though.

One thing I've found in my own use of AI, which Gowers touches on in his point at the end but which I think deserves more attention: AI makes some previously non-trivial tasks trivial, but that doesn't make the work itself trivial. You naturally expand the scope of what you attempt and take on harder problems than you could before. The floor rises, and so does the ceiling. The open question is whether that still holds once models can also do the harder problems, or whether choosing and framing those problems remains the human part.

Would it matter if AI had a proof for RH or P < NP, but the proof was 1000 pages long that Leaf could verify but otherwise impenetrable by a human mind? We generally assume these are true already -- I am not sure a long convoluted proof puts us in a much different place.

why does a fields medallist not have enough money to have a blog that isnt festooned with ads? good god wordpress.