For what it's worth, most mathematicians are paid to teach, and the amount of research funding going into mathematics is relatively small. Plus, there are rare but important broader advancements due to pure and applied math that are hard to predict in advance (e.g., cryptography, compressed sensing).
Mathematicians also decide what to prove in their research - taste is not a skill we have RLVR'd away (yet, not claiming this is fundamental).
Of course, the field is being fundamentally transformed, it will probably end up looking more like experimental science in the future.
Do you think it’s possible to operate math research in a fully autonomous way (i.e. with no human expert involvement)?
As a software engineer, my mental model so far is that OpenAI made a gigantic (but potentially sound) pull request to the math community, and the mathematicians just did not have enough bandwidth to review and merge it.
If my model is correct, I guess it makes a lot of sense to fund mathematicians, because their lack of resource is the bottleneck here.
That works, as long as the math is not beyond the mathematicians. Besides that, since you make a pull request analogy: not all pull requests survive review, but generating them like this is cheap. Mathematicians are unlikely to submit pull requests that will be refused because they have a stake in the game: if they do so too often then their papers will no longer be reviewed as eagerly as when they were not submitting bs. The AI peddlers have no such limitations and will happily flood the receivers. As a result actual mathematicians papers run the risk of no longer being given enough consideration because there is this bottleneck you identified. So what will happen instead is exactly the same as what is happening in the world of code: they will engage AI to help with the reviewing. Before long the foundation of math will no longer be understandable by humans. This would be a loss imo.
Reading your comment, I’m curious if AI models will eventually “fork” mathematics. (Sorry for beating the same cranky analogy)
Like, not expecting human experts to review and merge their results, but developing math branches on their own. I guess it’s at least doable for applied math. For example, if AI agents find a fast method of prime factorization, they can demonstrate it by cracking RSA encryption. No human review required.
I’m less sure how it plays out for pure math, though. My intuition is fairly limited here.
I'm increasingly seeing people read something in a post that isn't there. GP said "Tao is mobilizing the community".
You can mobilize the community through guest posts that slowly nudge people towards accepting AI, so that they demand funding for AI for academics. Which he himself suggests:
You can also brute force the existence of a proof...
It is true that the biggest splashes have been from counterexamples and such, but I have seen many smaller examples of proving positive results in my own field.
Perhaps not superhuman yet but sufficient to completely upend the status quo. And I'm supposed to believe that this won't change in a year? or two?
Maybe, but what remains of the human professional mathematics will be unrecognizable (at least for those without tenure I guess). All of our credit assignment systems are breaking and access to computational/financial resources is becoming way more important. Math has been one of the most open academic fields but everyone is becoming afraid of sharing their ideas. Personally, my job has slowly been moving from open-ended brainstorming to prompting/digesting LLM output (or LLM output transmitted by grad students). And the students are so demoralized! Also, the academic funding structures which have supported math departments are looking less and less stable - I imagine many of them will shrink.
mostly jk, although agents themselves are of course getting better at detecting whether a formal spec is faithful to a natural language spec
reply