Viewing profile — nicf

I'm a private math tutor specializing in exactly this sort of material, and I agree with this very strongly. Knowing what "counts" as a proof is one of the most common gaps I see i…

This sounds like a fully general argument against being alive and having experiences; you could equally well call love a "brain hack". I also care a lot about solving practical pro…

I've been working for a few years now as a private tutor teaching proof-based math to adults. Maybe this should give me an incentive to join in on some of the cynical replies this …

This was definitely something I saw on HN, but for what it's worth, in my conversations that night with other mathematicians no one brought up Lean proofs or peer review even as a …

I worked as a research mathematician for a while, and I've published peer-reviewed math papers. Reading this tweet put me in the strange position of feeling like defending the way …

No, what I'm saying is that I don't agree that taste in mathematics is more uniform than taste in coding! Mathematicians argue about taste all the time. Just as you might look at a…

If your complaint is about the type of work that gets you published in a fancy math journal, then I'll happily join you on the barricades. Sure, getting a paper into Annals of Math…

I've spent some time working both as a math researcher and as a software engineer, and I think this comment actually underrates the similarity between the two fields as they're act…

I was trained as a mathematician and worked as a math researcher for a little while (now working as a private tutor), and based on my experience I'd say this description is basical…

Oh, I hope I didn't come off as talking down to you! As I said in another reply here, the intention behind this comment was pretty narrow --- there's a certain perspective on this …

I certainly didn't mean to dispute that! Formal proofs have a lot in common with code, and of course reading code is illuminating to humans all the time. I meant to be responding s…

I don't know enough about the RH examples to say what the answer is in that case. I'd be very interested in a perspective from someone who knows more than me! In general, though, t…

I'm a mathematician, although not doing research anymore. I can maybe offer a little bit of perspective on why we tend to be a little cooler on the formal techniques, which I think…

For the articles on my website, I have a pretty janky workflow where I write a LaTeX document that I compile both to a PDF and (using Pandoc) to HTML, which I render with KaTeX. I'…

Yeah, that's definitely right --- an explicit counterexample to the Riemann Hypothesis would be very surprising and interesting, and I think that would be equally true no matter wh…

Woodworking is very far from my world, so I don't really have any grounds to judge how comparable the two things actually are. I'll say two things instead. First, right now presuma…

Incomprehensible proofs are indeed still useful to some extent, and I don't think you'll find many mathematicians who would reject them as an answer to the binary question of wheth…

I was an algebraic geometer when I was still doing research in the field, and it was definitely true in that corner of the world. Authors are alphabetical, and you usually cite the…

This is actually a metaphor I've used myself. I do think the woodworking community is both smaller and less professionalized than it would be in a world where industrial furniture …

Hm, good question. It depends on what you mean. If you're asking about restricting which theorems we try to prove, then we definitely are cutting ourselves off from vast swathes of…

This is an interesting question! You're giving me a chance to reflect a little more than I did when I wrote that last comment. I can only speak for myself, but it's not that I care…

oersted's answer basically covers it, so I'm mostly just agreeing with them: the answer is that you use a computer. Not another AI model, but a piece of regular, old-fashioned soft…

I would love that too. In fact, I already spend a good amount of my free time redundantly learning the mathematics that was produced by humans, and I have fun doing it. The thing t…

Especially not mathematicians! No one goes into math academia for the money, and people with math Ph.D.'s are often very employable at much higher salaries if they jump ship to ind…

Well, it depends on exactly what future you were imagining. In a world where the model just spits out a totally impenetrable but formally verifiable Lean proof, then yes, absolutel…