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.

https://lean-lang.org/

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:

https://en.wikipedia.org/wiki/Abc_conjecture#Claimed_proofs

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.