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.
Yes, so if there's useful math, you throw the LLM at it and use the results, no humans needed.
Humans can try to extract some ideas from the million line lean proofs, if they want to, I guess. But I can't imagine anyone really funding the human part of it.
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.
> With hindsight, some of my past rejections have become amusing. With a coauthor, I once almost solved a conjecture, establishing the result with an "epsilon loss" in a key parameter. We submitted to a highly reputable journal, but it was rejected on the grounds that it did not resolve the full conjecture. So we submitted elsewhere, and the paper was accepted.
> The following year, we managed to finally prove the full conjecture without the epsilon loss, and decided to try submitting to the highly reputable journal again. This time, the paper was rejected for only being an epsilon improvement over the previous literature!
Uh, care to explain? I have several colleagues that stopped submitting to journals once they reached full professor. They only submit papers from their students for the benefit of their careers. First-author papers, not so much.
Touche, I used to work in pure probability where that ridiculous Hardy-Littlewood rule used to cause all sorts of problems, but now work in statistics, where it is no longer an issue.
To be clear, the colleagues I am referring to mostly work in math phys. They are sole author papers, but I refer to them as first author, since that is the language I am now accustomed to.
And no, the culture in maths vs. theoretical stats is not really that different at the end of the day, and the latter is most assuredly like other STEM fields. I still collaborate on pure math papers (geometric analysis and PDEs mostly) from time to time, and it isn't really a different head space. My name is typically later in the alphabet, so I never even think about the alphabetical ordering.
Latest rumor is that 3.5 pro was struggling to be meaningfully better than flash, since iterations on flash were moving much faster than iterations on pro, likely due to model size (flash is estimated to be in the 200-400B range).
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.
Sure, why not? The founding charter of every D1 football school claims that it is a non-profit organization dedicated to the advancement of education.
It is still a mystery to me how recruiting "student athletes", with well below-average academic qualifications and superior athletic qualifications, giving them full-ride scholarships (which can be revoked if they fail to perform on the field) and allowing them to take the easiest courses (with dedicated tutoring staff looking over their shoulders), all while paying coaches the highest salaries on campus and using ticket sales to fund ever-bigger stadiums, has anything at all to do with education.
Perhaps the connection to education is that it is meant to be an object lesson (for the rest of the student body) in how to spot corruption and hypocrisy within power structures.
So I see two paths forward: Admit that the whole thing is a sham and just pay the football players their due; or turn legit and take the big money out of college sports by having actual student-athletes (who are students first).
To me it looks like he’ll be in a position to actually be unhobble DeepMind - reminder DM was sitting on a ChatGPT product for a whole year before ChatGPT got released (LMChat) and Google didn’t let them release it.
> DM was sitting on a ChatGPT product for a whole year before ChatGPT got released (LMChat) and Google didn’t let them release it.
Heard this multiple time, to me this is pure history rewriting and post-rationalization.
OpenAI also had a internal chat app before chatgpt, Microsoft had multiple, a bunch of other players also had internal chatgpt equivalents + many startups built some using OAI API.
The breakthrough of ChatGPT wasnt because OAI were the first to think of that (absolutely obvious and basic) product, it was because they were the first to get a model strong enough to be actually useful to talk to, vs a mere fun novelty.
There is no evidence whatsoever that DM ever had such a model that they decide not to talk about/release.
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.
To be fair to Nielsen, she is a worthwhile person regardless of her academic successes or failures; this point only does her a disservice to suggest that her words would be better ignored without it being made.
'we couldn't follow the law because the law's hard, instead we started the gateway for Trump by bending the rules, destroying norms, pretending the meaningless has meaning and creating pretext Conservatives could use for ignoring (first) these fake rules, but later under Trump huge amounts of the the real rules.'.
It was a bullshit agreement, and everyone knew it was, and were knowing in that what they were doing would weaken/damage politics in the USA and adherence to the rules. And they did it anyways. To no productive end but lots and lots and lots of damage.
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.
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