the conservationist in me wonders if the AI vs human discourse will stir some reconsideration of the 'intrinsic value of species and biodiversity' among some who dismissed it earlier

Well worth reading (as with all of Frank’s writing): galoisrepresentations.org/20…

I'm requesting all scientists in academia especially to seriously consider, discuss & test alternative approaches instead of shoving our heads deep in the ancient sands desperately clinging on to the old system. 4/

Today, we are announcing our third cohort of residents! Each resident will receive up to $2M to work on a high impact scientific problem, with the governing principle being that they build something people actually use and build it openly.

Without commenting on the correctness of this claim, I want to briefly say a few words about what it would mean in practice. Chess is supportable as a hobby in part because one can pick up the rules of chess in an afternoon. While one can't quickly play at a high level, it is relatively easy to appreciate the game, and have fun at it. Research math is not like this. Over the last decades we have made incredible progress understanding basic concepts (number, shape, etc.) but the edifice we have built to do so requires an incredible time investment. Learning the ideas that go into proving, or understanding the proof of, basic statements like Fermat's last theorem requires years of institutional support. It's possible that soon, AI will be able to do work at this level; despite recent successes, this isn't the case yet. But even if it can do this, why would it? Without people who care about these deep but fundamental ideas, who will ask it to? Perhaps it might on its own, or a person asking it to "do some cool math" might elicit a similarly deep idea, but who would understand it, if doing so requires years of unsupported work? In practice, turning pure math into a hobby means the end of pure math, and the end of people who understand basic mathematical concepts at a deep level. Whether this is something we want is something we'll have to decide together.

Please repost: My department (quantitative and computational biology at the University of Southern California) is hiring a teaching-track faculty member. The new hire will focus on teaching statistics courses to biology students. Apply by Dec 1 usccareers.usc.edu/job/los-a…

we made ai to solve millennial proofs and it immediately encountered the hardest unsolved problem in academia: who gets the credit

To wish that mathematics becomes like the human genome project is to wish that mathematicians not understand mathematics. Because one thing the human genome is most definitely not is "fully classified".

So there's a mathematical question I've been thinking about on and off for about 10 years. For the first 5 or so years I made very little progress, but learned a bit about the general area (while working on other things). In the last 5 years I've made some modest progress with collaborators, resulting in some (IMHO) nice results, though the question itself is still totally open. This has developed into some not-quite-rigorous research program which guides much of my current work (some of which is aimed at trying to make it rigorous). Of course I discuss this work with the models; for the first time, this week, I had a model produce, non-autonomously, a very nice partial result towards a question that came up in the course of this program, connecting it to various areas about which I know relatively little (microlocal sheaf theory, Lagrangian Floer homology). So now I get to learn about some of this stuff! Even in this (quite small) part of the project, there's lots for me to do--I've already found various improvements to and simplifications of the arguments it produced, and noticed some implications it seems to have that seem to me quite significant. An arguably underrated part of math is "discovering interesting new phenomena," and one function of mathematicians and the mathematical community is to certify this interest. That our open problems have been so significant to frontier labs is evidence we're pretty good at this! Of course I have thought about how I would react if GPT-8 Ultra Extreme or Claude Cthulhu 7 were to autonomously solve the entire problem. I think I would be excited--there would be a lot to learn, and surely a solution would raise many new questions. Maybe it would be a little bittersweet (I have an ego), but I view this problem as mostly an excuse to think about some fundamental objects, and I am quite convinced I'd continue to think about them.

I wonder how much of the divide among mathematicians on AI comes down to which of us consider ourselves scientists and which of us consider ourselves artists. (I'm very much in the former camp but for what it's worth I am sympathetic to the latter.)

I've been saying for some time that we should use AI systems to produce better work, as opposed to, say, more PDFs. One simple thing we can now do is identify and fix lots of extant errors in the literature. 1/n

Had a very optimistic discussion with a math professor friend about the role of AI in research. His take: 1) Having a fast way to disprove conjectures is already very useful and will save mathematicians lots of time. 2) Humans are very good at moving to higher levels of abstraction and will likely integrate AI proofs as a new abstract level that they operate over. 3) Out of necessity, math has operated on claims that can be explained by/to humans but surely there is an even bigger swath of math that cannot be explained to humans but is useful for other human goals. Having AI that can understand and verify those components and turn them into tools for human use could be revolutionary. The less optimistic discussion was over whether the games that humans set up for ourselves to stay motivated (challenge problems, medals/awards, etc) will be maxxed out by AI in a way that is ultimately detrimental.

Some initial thoughts, and a complicated mix of feelings. 1. Wow. I mean, Erdos problems are cool (I genuinely mean that), I didn't know about the Jacobian conjecture before it got disproved. But this newest batch from OpenAI hits home in a way the previous announcements did not. New circuit lower bounds? A simple, easy-to-describe non-sofic group? Hardness of approximation for CVP without needing a unique games-like conjecture? I didn't just hear about these problems from my friends or from seminars. I feel their importance in my bones; I deeply care about the answers to these questions.

Starting to think that the base rate at which well-known old conjectures are true might not be very high!

Openness to immigration has on balance been a huge source of strength to the United States but it can be a problem when you get immigrants like Elon Musk who fundamentally reject American values and ideals.

Please don’t vibe code science without checks, part 351. Treat agentic coding as a hyper-productive computational grad student who is drunk 1/4 of the time they aren’t given explicit directions.

If I were a conservative woman I think it would really give me pause that so many conservative men so openly despise women and believe they are not morally or intellectually the equals of men and should not be considered on their merits for positions of power.

I wanted to like QED's new 1% preprint ranking. But the more I looked at the data, the more uncomfortable it made me. Here is my full peer review: open.substack.com/pub/blekhm…

reupping my challenge to @JDVance

I wrote about AI in academia. "PhD-level thinking", LLM bias, grunt work, alignment, AGI, data center water use, AI politics -- something for everyone.