Comment by klyrs | Hacker News Reader

Comment by klyrs | Hacker News Reader

As a computational mathematician... I should clarify; I write programs to construct and verify proofs in discrete mathematics, and also I'm a hacker obsessed with high performance code... I agree that mathematics is in crisis. Why? Because I'm an oddball rarity. My first supervisor was a hacker too, but my PhD supervisor thought I was a wizard. Professors, by and large, can't hack. Those who could, abandoned the field for CS. Students are rarely hackers - often the celebrated kids are groomed through Olympiad, then Putnam, and jump straight into grad school with nary a glance towards a computer -- until they are broken against the only language seen as practical: latex.

Mathematics is innately about computation; every "proof" is an algorithm in disguise, and yet the field fails to attract talent because computation itself is treated with such disdain. Math has its own reproducibility crisis -- we don't write code that performs the tedious operations "left to the reader" and even when we do, journals won't post it.

And I don't see a ton of progress. My old department has hired a few young professors since I graduated... none can hack. It's sad

I totally disagree. I’m an amateur mathematician who dropped out of his PhD program at NYU with a Master’s. But I remember when I was doing my math major ever since college, seeing the Appel and Haken proof of the four color theorem and thinking it wasn’t a real “proof”, only a “half proof”. Because it just came down to a computer checking thousands of cases. The “last mile” was not proven.

Proofs are basically being able to explain something with a small number of concepts at every step. That’s the human way. What we lose when we turn everything over to ML is the ability to understand anything. And I don’t just mean by humans. I mean by machines too.

I can accept that human logic and thinking is just whatever we can fit into a small vector, and small bandwidth. If that’s all there was, and understanding was synonymous with pattern recognition, then machine learning would just be an amazing upgrade to that, with far larger vectors and so on.

And although there may be a “superlogic” out there where each statement involves millions of variables, I do not think we are achieving “reasoning” using this logic when it comes to computers. A project like “Cyc” tries to do it. But Machine Learning is something completely different.

For the real world, the results have been undeniable. So far MCTS is king, followed by RNNs and gradient descent I think. And these may actually be really good for learning situations.

But proofs are supposed to be more elegant. In mathematics, the whole explanatory elegance is in the “bandwidth” at every step of how many concepts you invoke. The question of “Why” something is.

MCTS simply seems to say “well, dunno why it is but in these 927282781618 cases things just seem to be worse than in these other 91273737833738 cases”.

Although I am open to the idea that a lot of human learning doesn’t really have the “why” explanation either. Maybe “why” is out of place to ask in many questions. But NOT in mathematics!

Appel and Haken were pioneers in the field of computer proofs. They didn't do it to modern (or contemporary) standards, and it did leave a bad taste for those who seek "elegance" in proof. Since then, theory and practice have advanced in strides; but we may have to agree to disagree on the thrust of your post.

I'd strongly recommend Gonthier's treatment of that particular theorem. In my opinon, [1] is beautifully written and illustrated; a shining example of how computer proofs should be written... and [2] is the actual proof.

> What we lose when we turn everything over to ML is the ability to understand anything.

Yuck, we agree here.

[1] https://www.ams.org/notices/200811/tx081101382p.pdf [2] https://github.com/math-comp/fourcolor

Mathematics may be innately about computation, but hacking is in large part about social constructs. I wouldn't be at all surprised if the same mental tendency that causes one to appreciate the beauty and elegance of pure mathematics, also causes one to flee in horror away from the computing edifice we've built so far.

I have no idea what you mean with hacking or hacker in this context

program

"Learn to code", perhaps.

Does anyone mind explaining what exactly this "Learn to code" saying is implying and where exactly it came from? At first glance, it seems pretty innocuous, but apparently a great deal of controversy has surrounded this statement recently. Is there some sort of hidden meaning I should be aware of here?

https://newrepublic.com/article/153019/fetid-right-wing-orig...

https://www.theringer.com/tech/2019/1/29/18201695/learn-to-c...

Christ. Nary a day goes past without me learning about yet another malign 4chan incident. To think I used to find them amusing.

This is literally Hacker News, I assumed that would be obvious. There's more to the culture than programming. There's two types of programmers: those who learn the grammar, and those who learn the interpreter / compiler.

Best description I’ve seen! Can sometimes see it in the bimodality of the types of comments too.

But that’s wrong.

To clarify, are you saying you've met people who have been successful at Olympiads and the Putnam who fail out of grad school because they can't learn LaTex?

Yeah, that seems very odd to me. I sat next to a successful math Olympiad student in first year advanced algebra. He typed his lecture notes in LaTeX in real time, producing textbook-like results on the fly. It looked like he was running Linux on his laptop. Suffice it to say, I think he could accomplish anything he wants to with his math and computer abilities.

I'd be shocked if that's the case. Basic LaTeX isn't that hard to learn, and the basics will take you really far.

> Basic LaTeX isn't that hard to learn

Basic LaTeX is probably not that hard to learn. But LaTeX is a really deep rabbit hole and you need a lot more knowledge of it if you write math papers.

You don’t have to go very far down the rabbit hole to write papers. If you can draw a commutative diagram, and insert a PDF graphic, there isn’t really anything much more complex than that.

> If you can draw a commutative diagram, and insert a PDF graphic, there isn’t really anything much more complex than that.

Not true. I know what I am talking about since I work in mathematical research (I like math, of course, but I openly admit not to like LaTeX).

Well, I’ve been to grad school, done significant amounts of mathematical writing, read my share of papers, so I know what I’m talking about, too. The depth of the rabbit hole isn’t that deep for any one person; it’s more like a gopher hole, but everyone has their own little gopher hole.

Could you give an example where advanced LaTeX skills is required to write a paper?

- TikZ wizardry.

- Often, I had to look deeply into forum posts to get LaTeX to format a formula in the way that I imagined (often the solution involved deep LaTeX wizardry)

- Creating a document that involves text in multiple alphabets (e.g. Latin alphabet, Greek alphabet, cyrillic alphabet). Actually trivial with Microsoft Word. ;-)

Not to even mention problems where I have no idea how to start such as how to do reproducable build processes for LaTeX documents (i.e. each run of the build process produces a binarily identical PDF document).

> - TikZ wizardry.

Yesssss

Tikz: don’t do that. Either use an editor that spits out a Tikz snippet (https://tex.stackexchange.com/questions/80418/list-of-tikz-e...), or draw your figure in Omnigraffle or something, export to PDF and insert the figure that way.

Multiple languages: \usepackage{babel}

lol no, nobody (within epsilon...) fails because of latex. But they aren't exactly endeared to programming as a result of the experience. I came from the other direction -- a hacker who had a dozen programming languages under her belt, including bf and Perl, before I was introduced to the moderately arcane latex.

They're quite frequently brilliant mathematicians... but far too often, they're steeped in the "pure" math culture that favors pencil over keyboard. In the context of this crisis, my opinion is that their education is not preparing them for the future. They succeed in academia... but their work is too often unverifiable.

It probably doesn't help that all of the proof tools I've seen are incredibly obscure and unrelated to any formal techniques taught to human beings.

Oh God latex breaks them? They should just use Lyx. I could take physics notes on a cpu faster than the profs could copy their notes.

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