Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Math writing is dull when it neglects the human dimension

golem.ph.utexas.edu

Post reply on HN
Print view View original

101–110 of 186 posts

Re: Math writing is dull when it neglects the human dimension

#101

Post by gosub100 »

Dalewyn wrote: post #52
saithound wrote: post #30

Earlier quoted context omitted.

This is good advice, but for a very different problem. 1. The problem in math is not that the way the "orthodoxy" insists on presenting things in a suboptimal way, but that if the reviewers find a good explanation of your result, they'll recommend that you publish in a lower-ranked venue than your result would ordinarily merit (at least unless you solved a famous problem). So researchers are incentivized to make the…

I've always found math is taught in the most daft, bland, vapid, worthless ways imaginable and I've thought it had to do with those who do the teaching: The teachers and textbooks. But reading this comment chain, am I correct to understand that this problem stems from the very essence of math itself? The people who live and breathe math just fucking hate sharing their passion with others? What the hell.

Could be the hazing mentality: I suffered to get here, why should I allow others to get here without suffering?

Re: Math writing is dull when it neglects the human dimension

#102

Post by GTP »

humansareok1 wrote: post #98
mycologos wrote: post #10

As somebody who works in a mathy subarea of computer science, oh man, I agree. My heart always falls when I need a result and it turns out the original paper is some terse typewritten notice from the 70s whose first sentence is a definition with a bunch of proper nouns and whose main theorem is given at the most general possible level with no applications at all. I have talked with math people about why this is, and…

>whose main theorem is given at the most general possible level with no applications at all. Outside of Applied Math why would this be an expectation at all?

Maybe OP means "application to a concrete example" to help the reader understand. If a paper is presenting a theorm, seeing it applied to an example could actually help.

Re: Math writing is dull when it neglects the human dimension

#103

Post by Ekaros »

mayd wrote: post #34

Some possible counterarguments: 1. Mathematics is a lot more abstract than it used to be. 2. Mathematics is a lot more specialised than it used to be. 3. Non-mathematical content is inaccessible to those who don't read English. 4. Space in academic journals is too precious to waste on inessential content. 5. The style is part of a universal mathematical culture so you should fit in. 6. There are many alternative plac…

For last point. Maybe the universities should step up and use that massive administration machine they have build for this publishing. Just post it on one of their websites. Link to the original paper in the prestigious journal.

Re: Math writing is dull when it neglects the human dimension

#104

Post by j2kun »

TBH I like both. There's a need for food writing and story telling, and a need to cut through the fluff and get to the main, precise result you need to know. I oscillate between adoring good writing and adoring Erdos' 3-page papers that get straight to the point.

Re: Math writing is dull when it neglects the human dimension

#105

Post by curtainsforus »

yau8edq12i wrote: post #31
js8 wrote: post #28

IMHO it's even worse. Once we figure out P vs NP, we will understand what it means to invert boolean functions algorithmically, and all mathematics will be replaced with an automated process. Today, most of the math is figuring out how to solve an equation, i.e. to give an algorithm to calculate the solution. We then "quantize" the algorithm to a state machine (e.g. convert reals to floats, algorithm steps to machine…

> IMHO it's even worse. Once we figure out P vs NP, we will understand what it means to invert boolean functions algorithmically, and all mathematics will be replaced with an automated process. I'm sorry, but that's just naive techno-solutionism. Maybe the computer will be able to solve your syntax problems, i.e., write proofs. It will never know anything about the semantics. Said differently. Maybe the computer will…

Strange, for you to say this in the age of transformers. They are obviously not there yet, but it seems inevitable to me that e.g. gpt 'understands' things better than a markov chain, and that future systems will understand more.

Re: Math writing is dull when it neglects the human dimension

#106

Post by gravescale »

gumby wrote: post #33

The author may well be on to something but personally I hate "story mode" in popular science books, and would really hate it in actual science papers, both the ones I read for work and the ones I read for fun. I want to go straight to the equations -- often I prefer them to the graphs. But (not joking here) this is a perfect opportunity for an LLM -- two opportunities, actually. LLM A takes a dry paper and gives it c…

I think a lot of it comes from following advice similar to "Write a Catchy First Paragraph" and it goes too far. You end up starting out with bizarre barely-sequiturs like "Fiona was a graduate student in lower New York in a family cafe run by a man named João sipping her usual order of single-origin cappuccino on a rainy Wednesday" before we even find out what the article is about, let alone what the actual insight is.

Furthermore, a lot of popular science ends up using the people involved as the lens through which the ideas are eventually viewed. Which makes a lot of sense for professional writers who are probably more attuned to the human interest than technical people. For an example, the first thing I did with a Lego vehicle model kit was to throw the little figurine into the "junk bits box" and proceed with a now-robotic model. Many things are more like Oppenheimer than Trinity Device Annotated Systems Manual. Which doesn't mean they're wrong, per se: the audience for it is probably bigger and the overall "utility" of the work is higher. And even a grump like me knows you shouldn't completely ignore human factors. On top of that, people who can write the complex technical stuff often don't want to mess about in the middle ground. But the bimodality is still annoying to me: people-centric "Stories" or deeply-involved dessicated technical material that I don't easily understand if it's not my field and not so much in-between.

Re: Math writing is dull when it neglects the human dimension

#107

Post by constantcrying »

js8 wrote: post #97
constantcrying wrote: post #86

Earlier quoted context omitted.

Some facts to consider: - Polynomial problems can still require enormous computing power to the point they are unsolvable. Even if tomorrow there is an algorithm transforming every NP problem to a P problem, not all problems will be feasibly solvable. A O(n^100) Problem is still P. - P vs. NP is about algorithmic complexity, it has no implications about mathematics being an algorithm or not. - The most likely outcome…

I think what's more fundamental than just answering P vs NP, is what exactly makes boolean functions hard to (pseudo)inverse? And it's the latter where answering (unless the answer comes from an oracle) the former will help. And this question is crucial, because everything we can ask computers (or restated, math with real-world applications) can be rephrased in terms of finding a solution to a SAT instance. It can be…

Do you not realize that SAT might just be O(2^n) at best? Even if by a gigantic miracle SAT is in P, unless there is another incredibly great miracle and it is something like O(n^3), which would almost certainly be the greatest discovery of CS, it would not replace almost any other algorithms? Simply because many of the most important ones are O(n^2) or even less.

>I think there might be a single algorithm, a SAT solver, which will subsume all others.

This is legitimately insane. You might as well hope for free energy, FTL Travel, or magic.

Re: Math writing is dull when it neglects the human dimension

#108

Post by constantcrying »

js8 wrote: post #100
constantcrying wrote: post #92

Earlier quoted context omitted.

>The outcome will matter less than having an answer. And I do think it will be a negative outcome either way, because it will obsolete lot of beautiful math, and replace it with a more mechanical process. The negative outcome will have exactly zero implications about anything. Except "turns out we were right all along" polynomial problems are just fundamentally less hard than problems you can verify the solution of i…

> Even is SAT is P that doesn't imply a solution can feasibly be found. It does, because in this case you also assumed that running numerical algorithm was feasible. So if your SAT solver fails to find the answer, it is either suboptimal method (because numerical method exists), or (if the instance is UNSAT) the numerical method gives you a flawed result.

Do you not understand that an O(n^100) algorithm is in P, but can never be run feasibly on a computer for any non trivial amounts of n? For n=10 you are already far beyond the number of Atoms in the universe.

I don't think you have any clue what you are actually talking about.

Re: Math writing is dull when it neglects the human dimension

#109

Post by Ekaros »

skhunted wrote: post #8
bedobi wrote: post #2

I’m no mathematician, so I only took basic school math, but I hated every moment of it. Mostly because overwhelmingly there was never any context or justification for learning any of it. Why does this exist? What actual real world problems does it solve? How did folks come up with and it, prove it works and start using it? Crickets. Just learn this formula, then that. The first time I heard the ancients calculated th…

I’ve been teaching mathematics for decades. Know how many students like the cool applications at the time they are taking the class? Very, very few. Usually, it’s later on in one’s journey through life that appreciation for the cool applications occur. At the time of taking the class doing cool applications inspires 1, pisses off 50 because it’s too hard, and leaves 49 rolling their yes.

At university level not insignificant amount of students are there because they have to. The course is mandatory. And they might only want to pass. They are not getting degree because they want education, but because it is perceived as needed in society. Now should these be ignored or not is a discussion to have.

Re: Math writing is dull when it neglects the human dimension

#110

Post by GTP »

protomolecule wrote: post #77
saithound wrote: post #24

Earlier quoted context omitted.

In my experience, (c) is a very large part of it. At one point in my career, I decided to try writing good, accessible articles, which properly motivated definitions and well-explained arguments with plenty of hand-holding. When I did that, a version of the derogatory sentence "The proofs are easy / non-technical." would appear in the reviews. Every. Single. Time. Of course, I have some independent confirmation that…

Yeah, when the result is easy to understand people think it was easy to arrive at. What surprises me that smart people don't correct for that bias.

Just my opinion, but I think that actually smart people appreciate the elegance of a simple solution to a problem that looks hard at first sight. It's the people that aren't so smart but want to sound smarter that are incentivized to make their results look harder than what they actually are.
Post reply on HN