Had one of those nights where all the vibe coded pieces collapse in front of you and you realize engineers are still very, very much necessary

damn, "Claude knows" is a pretty wild thing to say being an academic

10K PB on a random Tuesday. No bib. No chip time. Nobody cheering at the finish. But you just ran the fastest 10K of your life. Would you call that your PB, or does it need to happen in a race?

I cannot fathom all these “publicly funded hobby” comments about mathematicians. Any one of them could work as a quant or “AI Scientist” for millions of dollars, instead they scrape by on academic salaries for the benefit of humanity.

I wish people dunking on this understood that until now, "being a mathematician" involved not just doing math and publishing it, but being part of the whole institution, acquiring your place in society, a community, livelihood and so much more. The goal was to advance math, but you got all these other important things alongside it. AI decoupled that - now you can advance math without any of that. Replacing the existing thing blindly loses all the other benefits mathematics as an institution served our society and mathematicians are right to be upset about it. Should we reject AI for math completely? Surely not, but if you're going to replace a system, you should make sure you replace all the functions it provided, whether or not they were intended by design. This is of course not the responsibility of AI companies, but it underscores the need for societal-scale coordination for dealing with these disruptions

I think of my goal as a mathematician as something like: to better understand the fundamental concepts “shape” and “number,” and to convey that understanding to others. I think this is a valuable goal for many reasons. The primary reason discussed on social media is the (admittedly slow, but I think very real) diffusion of mathematical ideas into technologies that better our lives. There are others, though: production of human capital (which plays some role in this diffusion), and diffusion of mathematical understanding into culture, for example. It is not obvious to me that even the bare technological need for mathematics can be filled without human experts; this seems to me to be a tricky question of institutional design. For me the most compelling reason is simply that we feel a pressing need to understand. While deep understanding is largely limited to professional mathematicians, the existence of mathematicians and of the institutions they make up is a huge part of what makes mathematical understanding available to those who want it. I believe that the capacity to understand mathematics (and the universe as a whole) is part of a good life, and we should try to provide people with a good life. We operationalize the goal of understanding in a number of ways, problem-solving and theorem-proving among them. My own research is oriented around certain open questions that I believe measure our lack of understanding (of numbers, shapes and so on), and I think resolving those is genuinely important. I would welcome a solution with any provenance. But I think proof is only a measure of progress—what actually matters (for technology, human capital, culture, a good life) is a bit harder to get at. Crucially it is very hard to measure progress—plausibly theorem-proving is used in large part because it is easy to measure rather than because it is a perfect proxy for what we care about. I worry a bit that we may automate many easy-to-measure things without automating the correlates we care about for which they are proxies. This presents a clear problem for the design of institutions aimed at achieving progress. In part because I think problem-solving is a proxy for something else, I don’t feel that my goal of understanding “shape” and “number” is particularly threatened by a machine that is good at problem solving. I expect that machine to be a substantial boon, instead. Ultimately I think we will operationalize mathematical progress in better ways. But how to do this is a difficult question and I think many on here are too quick to dismiss concerns about it.

I am beyond irate by the scientists whose main reaction to the slopdrop is excitement about the results. The immediate priority has to be securing the pipeline for junior researchers. Otherwise, we will be the last generation of humans to understand, let alone do, mathematics.