Yeah, I'm also not a big fan of ghostwriting in the domains where it's prevalent. For what it's worth, though, academic writing is very much not one of those domains: taking LLM's out of it, if ten years ago it had…
You're proposing a new way that we could treat authorship that's different from how we currently treat authorship. There's an argument to be had about whether that would be better than our current system. My vote would…
I'm not the OP, but I can give my answer to this question, or at least one of my answers. This book is presented as being written by a human. (In this case, a human I happen to know, which would add another dimension to…
If it makes you feel better, I've known the author personally for over ten years, and he is both a human being and an excellent teacher. I'm about as confident as I could imagine being that he wrote this book himself.…
I read them as making a much weaker claim than this: not that the Lean proof isn't valid, just that it is not actually a formalization of the natural-language proof in the PDF they provided alongside it. I haven't heard…
By all accounts this result cost far more than a million dollars to produce, and either way OpenAI announced they won't be accepting the prize.
There are definitely some results which have this "a bunch of little hacks" quality you're describing, and while opinions differ I share your intuition that there's something a little disappointing about solving a big…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
Yeah, I'm also not a big fan of ghostwriting in the domains where it's prevalent. For what it's worth, though, academic writing is very much not one of those domains: taking LLM's out of it, if ten years ago it had…
You're proposing a new way that we could treat authorship that's different from how we currently treat authorship. There's an argument to be had about whether that would be better than our current system. My vote would…
I'm not the OP, but I can give my answer to this question, or at least one of my answers. This book is presented as being written by a human. (In this case, a human I happen to know, which would add another dimension to…
If it makes you feel better, I've known the author personally for over ten years, and he is both a human being and an excellent teacher. I'm about as confident as I could imagine being that he wrote this book himself.…
I read them as making a much weaker claim than this: not that the Lean proof isn't valid, just that it is not actually a formalization of the natural-language proof in the PDF they provided alongside it. I haven't heard…
By all accounts this result cost far more than a million dollars to produce, and either way OpenAI announced they won't be accepting the prize.
There are definitely some results which have this "a bunch of little hacks" quality you're describing, and while opinions differ I share your intuition that there's something a little disappointing about solving a big…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…