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Math writing is dull when it neglects the human dimension

golem.ph.utexas.edu

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

#111

Post by GTP »

light_hue_1 wrote: post #51
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…

> 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). Even if you solve a well known problem. I gave a talk once where I did so as a very junior student. During the Q&A a very well known senior person got up and basically asked me what's the point and this is all trivi…

Thanks for sharing your experience, but it leaves a bitter taste in my mouth: although well motivated, I find the outcome to be unfortunate. In an ideal world, people would appreciate the elegance of a simple solution to a seemingly hard problem. But, as you pointed out, the sad reality is that to some people, if your solution doesn't look hard, it reflects negatively on the importance of your result

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

#112

Post by ajkjk »

twelfthnight wrote: post #17

> Ideally the tricks I’m suggesting here will be almost invisible, affecting readers in a subliminal way Why would I want a math paper to be subliminally manipulating me? I feel like everyone has been watching too much YouTube/tiktok and is buying into the notion that clickbait isn't just a vicious feedback cycle destroying everyone's integrity.

I mean.. It's no different than a story being written better instead of worse. The dry paper is just worse in every way, at both the author's goals and your goals.

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

#113

Post by mycologos »

GTP wrote: post #102
humansareok1 wrote: post #98

Earlier quoted context omitted.

>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.

Yup. I don't mean "here's how you can use my theorem to build a bridge", I mean "here's an instantiation used to prove a more tangible result". Bonus points if multiple such results fall out of the general theorem. That's good evidence to me that generality is actually accomplishing something.

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

#114

Post by didntcheck »

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.

I guess it's analogous to the phenomenon of some people feeling "ripped off" when they pay a tradesman (or other worker) to do something that (appears) physically easy. As the apocryphal story goes "you're not paying me to turn a screw, you're paying me to know which one to turn" or "I could call my apprentice and have him take longer to do it if you'd like"

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

#115

Post by twelfthnight »

ajkjk wrote: post #112
twelfthnight wrote: post #17

> Ideally the tricks I’m suggesting here will be almost invisible, affecting readers in a subliminal way Why would I want a math paper to be subliminally manipulating me? I feel like everyone has been watching too much YouTube/tiktok and is buying into the notion that clickbait isn't just a vicious feedback cycle destroying everyone's integrity.

I mean.. It's no different than a story being written better instead of worse. The dry paper is just worse in every way, at both the author's goals and your goals.

> This may require “watering down” the results being described — stating corollaries or special cases instead of the full theorems in their maximal generality. Sometimes you may even need to leave out technical conditions required for the results to really be true.

This is a trade off, don't you think? Without the marketing, the paper would be more complete and correct.

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

#116

Post by Sirizarry »

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…

I’ve known a few very intelligent maths professionals and although good people, they always struck me as a bit robotic. I know it’s anecdotal and a small sample size but I wouldn’t be surprised if a certain personality is needed to excel and it just happens to be very terse and overly professional. I however also think that that’s a big reason I never got into advanced mathematics in the first place. I can’t stand terse and overly professional material. I get bored much too easily.

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

#117

Post by Someone »

somenameforme wrote: post #50
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…

This was my initial reaction as well, as I have complete disdain for the lowest common denominator approach to many things in modern society. But then something occurred to me - IMO one of the most well written scientific papers is Einstein's special relativity paper. [1] But it's absolutely a 'story mode' paper! A moderately educated individual could easily understand and follow the paper, even if they might not nec…

I don’t see this article argument for a “lowest common denominator” approach. For example, how is replacing

“Let M be a complete Riemannian manifold, G a compact Lie group and P → M a principal G-bundle.”

by

“One of the main problems in gauge theory is understanding the geometry of the space of solutions of the Yang–Mills equations on a Riemannian manifold.”

doing that? It gets rid of “Lie group” and “G-bundle”, but adds “gauge theory” and “Yang-Mills equations”

Also, “Of course, one should not give a detailed blow-by-blow account of every pitfall and wrong turn”, IMO, is an argument against doing that. It more or less says: “assume that there are steps your readers can make on their own”.

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

#118

Post by darby_eight »

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…

> leaving the dry bones for me to pick over and savour.

How would you understand the relevance the equations have to the overarching finding of the paper? Narrative is just as important in tying together apriori reasoning as it is in other contexts in all but the most trivial findings, and much of computer science is not, in fact, apriori, requiring argumentation to justify the abductive reasoning within.

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

#119

Post by js8 »

constantcrying wrote: post #107
js8 wrote: post #97

Earlier quoted context omitted.

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 sol…

> Do you not realize that SAT might just be O(2^n) at best?

Yes, but that's the worst case on all possible instances. Even with this worst case performance, there might be an algorithm that works on par with other algorithms that specialize only on certain instances. E.g. there can be an O(2^n) algorithm for general SAT which performs in O(n^(3/2)) on XORSAT. We simply don't understand the problem well enough to tell.

Also the set of worst-case instances can be vanishingly small in practice.

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

#120

Post by Folcon »

kd5bjo wrote: post #93
mycologos wrote: post #75

Earlier quoted context omitted.

The target audience point is fair. There are basic concepts that I don't bother defining in any paper I write, and I'm sure there are people who would make the same argument about them that I'm making here. But I'm not suggesting writing everything like "An Extremely Gentle And Slow Introduction to X, With Lots of Reassurances That You Can Do It". The question probably comes down to how accessible a paper should be.…

I’ve started to keep a collection of readable papers (mostly engineering/experimental science, but a little bit of more theoretical work as well) that cover what I consider to be pretty foundational concepts, because additional citations are ~free and it at least gives an entry point for readers that are on the edge of the target audience. As a consequence, I’ve read papers that were written anywhere from the late 19…

> I’ve started to keep a collection of readable papers

Are these shared / mentioned anywhere?

A resource like this would be super helpful.

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