As a mathematician, this is far from my experience of actual professional mathematicians, because they encounter people much smarter than them quite often. Maybe more true among graduate students, however.
It's hard to know what math is 'useful' a priori. That's always been the argument for supporting basic research. This is not why I am a mathematician however. I think there's intrinsic value into understanding something of depth and meaning, but the societal setup we have now that mostly agrees this is valuable is probably a very contingent phenomenon that is unlikely to last much longer.
FWIW even Astra hasn't been able to solve the problems I care about, which are less about proving theorems and more about understanding the right way to think about already existing stories (and thus permitting extensions to new contexts). However it's been a more than a capable interlocutor to test my ideas with and see if they actually have any content. It's also great for parsing possible mistakes in long technical arguments that at least my brain isn't wired to verify completely satisfactorily. Personally, I think it's good to know what is made trivial (meaning depending only on token expenditure) vs what remains a real hard kernel.
This is essentially irrelevant to the content of the post, but it's amusing to me that he casually mentions submitting to JAMS as if its acceptance were a mere formality.
The true morally correct path would have been to take big money out of college sports (not to mention high school sport) entirely. Of course this is now essentially impossible without what I imagine will be extensive rioting countrywide.
Maybe there's an error, but much of this write-up reads like nonsense to me. The assertion that a semidirect product with an abelian factor must admit that factor in its center is absolutely false. This is actually acknowledged later in this article, but is handwaved away in incomprehensible fashion.
If you think not having done this (or really anything else except somehow preventing him and the Republican party from gaining power in the first place) would have prevented any of Trump's actions, I have a lovely bridge that just came on the market that I think you would be the perfect buyer for.
Stark assessment: "The Trump administration hates academic science funding, full stop. They hate where that money goes, and they hate who it goes to. They want to keep all that money for themselves, to hand out to favored cronies who can help them get elected and to steer yet more money and more power back into their hands."
What this is yet another demonstration of how being immensely accomplished in one field says absolutely nothing about what one may be able to contribute to another.
Yes, as someone who prefers developing the 'correct' structure over 'merely' proving theorems, this is good for me in the short term. However, the writing I fear is on the wall for my medium and long term utility.
Speaking as a mathematician, it does seem like we're a bit fucked as a community. Anything that is at all accessible to currently existing methods and mathematical infrastructure is probably going to fall to the frontier models of today, and at this rate of progress it's likely that, already by next year, we'll see new infrastructure being put into place by AI, giving us a world in which a few designated interpreters of the oracle get to 'do' mathematics, while it withers on the vine as an avenue for the exploration of human meaning.
This is nonsensical: Properness of the map is equivalent to its being an isomorphism (quick proof: Jacobian invertible implies that the map is etale, and properness would imply that it is finite etale, but affine space doesn't admit non-trivial finite etale covers), so the lack of properness is just another way of verifying that this is indeed a counterexample.
This is of course an oversimplification by graduate students trying to reach a broad audience, but one could argue that it in fact is. Langlands himself viewed his program as part of an attempt to achieve non-abelian reciprocity laws. See for instance: https://www.phys.ens.psl.eu/~kashani/slides_chenevier.pdf
>The situation with human mathematicians is not much different. Eg, Wiles original proof of Fermat's Last Theorem contained errors found by reviewers, which he later repaired.
In fact, it was Wiles himself who realized there was an error.
I don't know the numbers, but you and the parent are saying different things. The US could still be supplying 2/3s of Israel's weapons while only subsidising about 10% of that supply.
”For example, it allows NSF to make awards to nontraditional recipients such as a limited partnership or a venture capital firm, some of which might have been created solely for the purpose of receiving the NSF award. It also allows NSF to make additional awards without the need to review a new application.”
FTA: The public comment period closes approximately July 13, 2026 (45 days from May 29 publication). Comments must be submitted to regulations.gov, Docket OMB-2026-0034.
This kind of comment might have been borderline reasonable before 2025 (though I would have found it laughable even then), but the evidence of the last 18 months shows that one side is in fact evil, corrupt and venal in entirely unprecedented ways.