6,338 karma · joined November 20, 2010
thorne [at] math [dot] sc [dot] edu
But having traveled around Japan extensively, I've had a very easy time buying train tickets in person, at the station. You can buy in advance if you want, but I've rarely had any need; just go, and buy a ticket for the next train.
So I guess I'm not too surprised to see that the website design is crappy: it's an afterthought.
Much of this money is going to Texas, and James Talarico (the Democratic candidate there) has not been shy about accusing Musk of trying to buy the election.
Sure, flying cars are cool. But I don't get the impression that Musk's politics have been forgotten at all.
By all means, please read the article if it's interesting to you and ignore it if it isn't. But I believe that it's mostly directed to those already within the research math community, with a far more important purpose than to be interesting.
As the post itself explains, we (research mathematicians, as a profession) need to coordinate on deciding what a bright future will look like in a world with powerful AI, and in plotting a course to get there. And we need to do it fast, or circumstances might decide for us.
Historically, we've rather sucked at coordination. We need leadership -- we need someone to step forward, and begin by floating ideas and getting the conversation rolling. Personally I am very grateful for what Tao is doing here.
Probably some combination of: some of the 372 problems were easier than the rest; the AI got lucky on these 372; there were existing papers out there in the literature which proved especially helpful for these 372; and other similar factors.
For example, if you look at Terry Tao's blog, he has a tremendous amount of first-class expository writing. So, too (to some extent) do junior mathematicians -- but, unfortunately, this tends to not be highly valued by the job market. Grad students and postdocs have learned that to succeed they need to play by the existing rules of the game.
Well, the board has just been yanked from underneath them. People like me can afford the sort of idealism and soul-searching that the parent comment describes, but junior mathematicians face a very unenviable set of circumstances.
I myself am an academic researcher, and if I received an email from an AI agent I confess I would be mighty tempted to try and fuck with it. Come up with some outlandish answer, just out of curiosity to see how it would respond.
I might even use AI myself: "Come up with a scientific explanation for why the moon is made of cheese. Your answer should be as preposterous as possible while using loads of scientific jargon, and written in the same style as actual science writing."
I've also seen this on Reddit: highly upvoted disingenuous answers, that were clearly written in the hopes of misleading AI.
Most people my age do have kids, especially given that I'm living somewhere fairly quiet. I like kids and get along with them well -- indeed, to the extent that I'd happily occasionally babysit for free. But parents seem to be living in a different world.
One difficulty is that most parents seem to be deeply invested in their home lives and daily routines, in a way that I find difficult to relate to, which can make small talk difficult. But one way or another, I should probably make some attempts to expand my social life.
Your (1) is most certainly true.
As for your (2), most mathematicians I know have at most a passing interest in formalization, Mathlib, and Lean. My understanding, which is admittedly quite superficial, is that AI is actually getting quite good at translating human-readable mathematics. I could be mistaken about this, but even if there is a lot of human work to do, it sounds like a lot of anal-retentive oversight of work you didn't do yourself -- the sort of task that academics love to complain about!
Perhaps human interest in Lean will grow, but I don't anticipate it occupying the attention of more than a small slice of the community.
Your (3) is an interesting question. I work on the theoretical rather than applied side, but what you describe might very well be true for applied mathematicians.
But external funding, e.g. from the NSF, also supports conferences -- and I suspect that few people would be willing to attend if they had to pay out of pocket. Without this opportunity to talk to one another, the field would be much worse off.
Different academic disciplines are very different, and most don't engage in the same kind of black-and-white problem solving that mathematicians do, where you either have solved a problem or you haven't.
But all insist that you engage in some sort of outwardly visible production in your field: books, articles, conference presentations, public lectures, exhibitions, performances, something.
We haven't yet figured out what that should be, but I presume that everyone would agree that this should continue. As one possible model, check out this blog post of Terry Tao's, where he gives his own perspective on the recently proved Jacobian conjecture.
https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the...
When computers can solve the underlying actual problem, this sort of work seems likely to rise in value, and be something which a greater number of mathematicians engage in.
And I think that's one important difference: with vibe coding you can't cast aside the AI after you've taken the initial step.
That said... most of us are not working on problems as famous as Navier-Stokes. Even if OpenAI could scoop me based on my back-and-forth with ChatGPT, which I presume they could if they threw $15 million worth of compute at it, I highly doubt they'd bother.
As a university professor, I've seen that all universities want to do everything.
By which I mean, they employ all sorts of people who are pushing a huge range of agendas. You can't meaningfully speak about "what universities want", because various factions tend to expect free rein to pursue their goals, and there is no mechanism to get everyone pushing in the same direction.
> it was Claude, with Levent Alpöge and Ava Howell!
Alpöge is the same guy who prompted Claude for a proof of the Jacobian conjecture.
Within academia, it is to your definite advantage to have your name associated with breakthroughs, for obvious reasons. Outside academia I don't have firsthand experience, but I'd have to imagine the same holds.
Exactly this. A fundamental question in the subject is, whether elliptic curve ranks are bounded. Contrast with e.g. prime numbers, of which are known to be infinitely many. If you set a new record for the largest known prime, then that's cool but everyone knew there were plenty out there to discover.
This paper, by leading experts,
https://arxiv.org/abs/1602.01431
made a significant impact in the field, coming up with a heuristic argument for why ranks of elliptic curves should be bounded. The same heuristic suggests, albeit more loosely, that we should perhaps be a little bit surprised to see a curve with rank at least 30. So it's mild evidence that the heuristic itself could be mistaken.
https://kconrad.math.uconn.edu/blurbs/
If you're interested in learning any of the advanced math topics covered here, pretty much everything Keith has written is gold.
But otherwise, mathematical proofs are read and written by humans, and at the end of the day the relevant standard of proof is what other mathematicians will accept.
Occasionally, mathematicians don't agree. For a prominent example, you can read about Shinichi Mochizuki's claimed proof of the so-called ABC Conjecture:
When I worked in fast food, in the nineties, the managers were under pressure to optimize a variety of metrics. But they didn't have a lot of carrots or sticks, and most of the rank-and-file employees put in an honest day's work but beyond that didn't give that much of a shit.
Sure, I said.
"On a scale of 1 to 10, how satisfied were you with..."
"Umm, can I just tell you why I cancelled my service, as if you and I were both human beings?"
"I'm sorry, I have to follow this script exactly."
So I apologized to the guy and hung up.
That said, picture someone killing a kitten and someone else killing a cockroach. One could prevaricate all day with highbrow reasons for why the first is monstrous and the second is perfectly moral -- but honestly, for most people, I suspect it comes down to the fact that kittens are cute and cockroaches aren't.
The issue, as I see it, is that elite credentials are overvalued, and that we live in a society which is becoming more and more unequal, and where housing prices in particular are skyrocketing.
Without solving that, the alternatives to the Ivy League (e.g. undisguised nepotism) seem to be even worse.
I had the impression they were essentially synonyms, and this was borne out by two university courses in philosophy which I took. That said, googling "morals vs ethics" turns up quite an interesting mess. A variety of contrasting perspectives showed up:
- Ethics come from an external source, whereas morals come from within
- Ethics are rational and structured, whereas morals are more emotional
- Ethics is a philosophy or code of behavior, whereas morals refers to beliefs and conduct
- Ethics and morals are used interchangeably
It seems nobody agrees on what the words mean. Which, on reflection, tracks. For me, the idea of an HR training session on ethics is laughable, but for someone who thinks of the word differently it could certainly make sense.
Yeah, if I'm calling or chatting with a company, I expect them to stand by whatever commitments they make, and I will judge them harshly if they don't. This is true whether an AI or a human is speaking on the company's behalf.
I assume that AI is quite capable of designing workouts, and creating audio files with instructions that I could take to the gym. But I have no interest in that; the appeal of the classes is the relationships I build with the other humans.
Perhaps this is overly optimistic, but I hope that it's the things that people actually value, where they find meaning and depth and human connection in the experience, that will prove most resistant to AI.
I joked to her that puppies beat SSRIs any day of the week, that she should write prescriptions to take to the animal shelter. And it's probably true! Unfortunately, I don't live the kind of life that's compatible with a pet.
Personally, I'm grateful that doctors mostly stay in their lane, although I would hope a good therapist might recommend physical activity to someone who needs it.
And as to what kind of exercise to recommend -- the advice I've heard is that the best kind of exercise to do is what you enjoy and will therefore stick to. Brisk walking three times a week for 20-30 minutes might work great for some people. But if someone finds that a tedious chore, they're probably not going to stick to it.
Yeah, I tried out an online weight loss program (Wondr) that made the same point. When it was video of psychologists, I could definitely understand what they were saying. Unfortunately, when it was video of a chef, saying words like "flavor" with great enthusiasm, I found it hard to stomach. Judging by how happy food makes many people, my loss I guess.
Something to think about anyway..... thanks for your input.