okay so. when a mathematician proves a random conjecture you are supposed to politely clap. this is because it would be rude and embarrass the mathematician to point out that most conjectures are not that important or meaningful when an LLM proves a random conjecture mathematicians are caught in a funny position where they want to say "these are not very important or meaningful conjectures and having magic proofs or counterexamples come out of nowhere is not particularly interesting or useful to anybody, except possibly the person who proposed the conjecture and some of their colleagues" but saying that puts them in an awkward position - why didn't they say that when humans were doing it? was nearly all mathematics actually pointless this whole time and mathematicians were just politely avoiding ever pointing this out so they could all still have jobs? if the best defense you can come up with of mathematics as a human endeavor is, effectively, "it's really fun for us to come up with these baroque puzzles and then solve them, don't screw this up for us," you are completely abdicating your responsibility as a public endeavor that taxpayers fund. i have occasionally argued that pure mathematics lost the plot decades ago and gave up on having any kind of meaningful relationship to the rest of the human quest to understand reality. this was a slow-burning tragedy, and mathematicians have been able to hide this state of affairs from everybody else because nobody else knows enough mathematics to critique what mathematicians are doing i saw a famous professor point out a few years ago that the machine learning that underpins AI is powered by 18th or maybe 19th century mathematics, you don't need much more than multivariable calculus, linear algebra, a bit of probability. he said this as if it was a dunk on ML and AI; imo it's a much bigger dunk on mathematics. you're telling me the most important scientific revolution of our lifetimes doesn't involve any of the math that mathematicians have been working on over the last century or two? you see how that's worse, right? (tbc i'm not saying that stuff is all useless, you need a bunch of stuff from the first half of the 20th century to do physics, e.g. functional analysis, lie theory, representation theory all feed into the standard model. after 1950 or so things get more dicey) if mathematicians still want to have jobs they are going to have to do a better job than they have for the last few decades convincing the public they do something that actually matters, and figuring out what that actually is or should be. this is an opportunity for the field to do some very serious soul-searching, as serious or more serious than the foundational crisis from a century ago. this kind of whining is absolutely not going to cut it