nicf

7 ms·

1.
by nicf 1mo ago
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 in students who come to me after self-studying
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by nicf 2mo ago
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 problems, but the reason it's important to solve
3.
by nicf 2mo ago
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 has gotten, but that's not actually how I find mys
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by nicf 2mo ago
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 joke. We just copied and pasted the polynomials into a
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by nicf 2mo ago
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 peer review works in my (former) field, which I'm
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by nicf 2mo ago
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 piece of code and agree that it compiles and does
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by nicf 2mo ago
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 Mathematics or whatever is more game than art in the sens
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by nicf 2mo ago
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 actually practiced. Some math research does involve g
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by nicf 2mo ago
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 basically right, with one extra wrinkle. In order to get a Ph.
10.
by nicf 1y ago
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 stuff that I see pretty often on HN that I think i
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by nicf 1y ago
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 specifically to the case where some future theorem-provi
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by nicf 1y ago
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, the answer to this question would depend on the spe
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by nicf 1y ago
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 I've said on HN before. I'm actually prepare
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by nicf 1y ago
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've been in the market for a while for something that&#x
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by nicf 2y ago
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 whether it was found by a person or a computer! The situa
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by nicf 2y ago
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 presumably the reason a few people still become master wo
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by nicf 2y ago
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 whether the result is true. But when you talk about &qu
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by nicf 2y ago
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 paper by listing them all, no "et al"'s. I t
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by nicf 2y ago
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 production didn't exist. (This is a bizarre counte
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by nicf 2y ago
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 math space, and we're doing it on purpose! The
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by nicf 2y ago
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 a lot about me personally being the first one to
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by nicf 2y ago
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 software that has much more in common with a compiler
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by nicf 2y ago
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 that makes me sad to imagine --- and again, this is not a pre
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by nicf 2y ago
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 industry. The reason mathematicians stay in the field ---
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by nicf 2y ago
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, absolutely, there's a lot for human mathematicians to do. But I
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by nicf 2y ago
The Four Color Theorem is a great example! I think this story is often misrepresented as one where mathematicians didn't believe the computer-aided proof. Thurston gets the story right: I think basically everyone in the field took it
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by nicf 2y ago
I'm a former research mathematician who worked for a little while in AI research, and this article matched up very well with my own experience with this particular cultural divide. Since I've spent a lot more time in the math worl
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by nicf 2y ago
Uses what?
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by nicf 2y ago
I'm a private tutor who works with adults on proof-based math. I've often had a similar thought to the one you're expressing here --- I also found proofs pretty revelatory when I first exposed to them and wondered where this
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by nicf 2y ago
You're welcome! There's actually one more point that I thought of after sending that reply, which since you mentioned it again I should maybe flag. Totally apart from physics, it may seem intuitively plausible that if you have a f

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