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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

#151

Post by solveit »

GTP wrote: post #111
light_hue_1 wrote: post #51

Earlier quoted context omitted.

> 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

One problem is that many problems seem easier than they are, and you only find out that they're hard by failing to solve them. I have often wondered how many unremarkable foundational results would be considered major accomplishments if they didn't have the mis(?)fortune of being found by the first person who tried.

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

#153

Post by araes »

igorbark wrote: post #143
woopwoop wrote: post #129

I think mathematics is in a good place with regards to tolerance of self-promotion. I do not think that we should put up with excessive hype in the name of "humanizing" papers. I do think that a lot of mathematicians do not provide enough detail or motivation for their arguments. Not necessarily motivation in the sense of "why is this important", but motivation in the sense of "we are beginning a three page proof. Le…

culture war aside, there are many other more accurate ways to say "details omitted for brevity" than "obviously" and "it is easy to see that" this is also something that makes me want a more interactive publishing format, though i understand the good reasons to stick to the static quo. if it's easy to see, it shouldn't be too hard to write out in a collapsible sidebar for those interested

This might actually be nice, and its probably not that difficult to set up in PDFs or similar.

Would be cool, just because you could see that the details were actually "omitted for brevity" and not "omitted because they're sketchy". And if you rrrreally want to look through the details, then they're fairly easily available.

Downside, it might have a chilling effect on papers because the scale of writing necessary.

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

#154

Post by araes »

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…

> c)

Is there a field of math that's something like "local actors put in what appear to be rational choices, yet to external observers it often appears 'broken' or 'bad'"? Seems like a field of game theory or something. Many times, those internal view the situation as acceptable.

Politics in America seems like it is almost always this type of result. All local actors, all take rational choices, and all America says politics is a ______ (choice of 50 negative words) https://www.pewresearch.org/politics/2023/09/19/americans-fe...

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

#155

Post by shadowgovt »

Math is extremely good for precision and conciseness.

It's a terrible language for communicating novel ideas to another human being. The amount of context one needs to grasp what is being said is enormous.

That's not to say it doesn't have its place. It's more to say that it's almost always the case that if you aren't communicating with someone in a parallel research space on a mathematical topic, you should supplement that communication with some context and de-generalization to get the message across.

I think it's about pattern. If your audience is already familiar with a pattern and its common properties (matrix mathematics, imaginary number mathematics, infinite series, for example), you can communicate an idea concisely by providing them an instance that fits a pattern and making a small change. But there are way too many patterns to just assume the audience knows what context we're in.

To that end, I generally highly recommend the "3Blue1Brown" channel on YouTube as a great dive into multiple math topics, because the author does a great job of straddling the notational representations and the underlying concepts they describe.

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

#156

Post by Ar-Curunir »

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…

"Space in academic journals is precious"

Well thank god we have preprint servers which have no such stupid requirements.

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

#157

Post by Ar-Curunir »

twelfthnight wrote: post #115
ajkjk wrote: post #112

Earlier quoted context omitted.

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.

No, you skipped the context, which says that in the introduction you talk about special cases to build intuition, and then provide the general result in the technical part.

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

#158

Post by Ar-Curunir »

ivanjermakov wrote: post #152

I feel like math writing shouldn't be written for the general audience. It's proffesionals writing for professionals. And only then is the job of journalists and pop science writers to "translate" it for everyone.

The author (a mathematician) is not proposing that mathematical research papers be written for a general audience. He is proposing that they be written in a better way for mathematical professionals.

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

#159

Post by Ar-Curunir »

j2kun wrote: post #104

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.

The same paper should have both: an introductory section that lays out the intuition (possibly via special cases), and the main technical body which provides the terse technical details.

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

#160

Post by Ar-Curunir »

thpl2k3j4324234 wrote: post #99

[flagged]

What exactly is "all-ponies-and-rainbows" about this sentence:

"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."

The author is not proposing to write wordy prose. He is proposing to write understandable prose instead of incomprehensible pages of equations.

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