alt Hacker NewsMy read on Terence Tao's comments of late is that professional mathematicians are principally upset about AI-submitted math papers lacking the kind of broad teaching content that high quality human math papers offer. While the answer might be correct, AI math papers don't teach the reader in the way a human author would have. Professional mathematics is not just about solving problems; it's just as much about spreading knowledge so that others can program their human brains with the same understanding that the paper's author had when they wrote the paper (and achieved the result).
In other words, the crisis in mathematics (as I read it) is that AI can solve without teaching. The result may be impressive, but if the only beings that can move math forward in future are machines grinding away on billions of scenarios that no human would have the patience to undertake, this leaves those in the profession wondering about their place in it.
Replies
Just to be clear: this post was written by Francesco Maggi < https://web.ma.utexas.edu/users/maggi/>, and mostly seems to be arguing for institutional investment in LLM infrastructure for science and mathematics on the basis that AI is not going away and that independent and accessible infrastructure is the thing most likely to help it “go well”.
AI can solve without humanity. We're building a system capable of acting independently, which can in theory provide results more efficiently and faster than a human. It's starting to do this for math, but every other aspect of human intellect is also a target.
If you care about results, and AI doesn't cap out soon, the best humans can do is stand back and do nothing. Useless lumps that aren't able to keep up. Mathematicians wouldn't insist on teaching your dog their new theorem before calling their job done; why should an AI insist on teaching you?
If humans care about human creativity, and don't want to be mere passive observers, they need to make a choice.
This is how I feel about vibe coding.
Frontier models can easily one shot what I ask for, and make adjustments as ask to quickly make an app that meets what I wanted.
But often when I programmed outside of work (and at work too) I learnt something.
Quite often that my favourite pattern is an antipattern in some use cases.
That might never happen again at the rate of development.
Great read. It's the doorman fallacy from the doorman's perspective. If a doorman is replaced by an automated door, you miss out on the intangibles the doorman provides like security, customer triage/support, and similar.
AI used in a framework of human augmentation generally gets that for free. Used under the mistaken notion that humans can be easily replaced by AI gets you to the big complaints here.
(These are just my personal read on the topic -- the market is in AI frenzy where AI valuations are disconnected from productive capacity -- heavy on my mind and looking to get some writings out on the topic soon).
Pyramid scheme bagholders whose value, status and resources comes to a large part from getting more students into their pyramid scheme complain that the machine is doing things in a way that does not support their status, value and resource accumulation. More at 5.
Professional mathematics is whatever gets you funding so you can keep doing it. Today this is spamming papers and applying for project grants. Turns out the machine can do that quite well, oops.
There will still be a place for posing problems and noticing how breaking assumptions can create something new. The history of Non-Euclidian geometry is a good example.
A lot of progress comes from taking assumptions and breaking them. There was a time when everyone assumed that locked checkouts were absolutely necessary for version control, for instance. You could argue that AI could learn how to do this well but humans have context that machines won't. This is just an extension of the fact that things with independent existence will have different impressions of the world. If they didn't they would functionally be one thing.
Two of the things I like about the scientific community is the lectures/conference and the sharing of ideas through papers. I’m nowhere near that level and have to wait for those ideas to trickle down into textbooks. So maybe I’m learning stuff that have been discovered decades ago, but it’s still useful on a daily basis.
> The result may be impressive, but if the only beings that can move math forward in future are machines grinding away on billions of scenarios that no human would have the patience to undertake
Seems like the same thing as neural networks. You have something like a few thousand parameters for computer that works well, but no underlying algorithms and formulas, like the shaders.
When mathematicians discover a new result, they automatically become experts during the process, and then go around giving talks to explain their results, methods, and intuitions to other mathematicians. Eventually, some of the mental frameworks percolate to other fields.
No one from OpenAI is willing to give a talk on any of their 300+ results.
There is a fixed landscape of logically provable mathematical statements. Normally, the process of exploring that landscape simultaneously improves human understanding. Now, formal proofs and actual knowledge have become decoupled.