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 the proofs weren't easier than in any of my other work (e.g. my coauthors and I had to work just as hard to get them), but this led to having to resubmit them to less prestigious journals than the ones which normally published my work.

I gave up on this approach, and realize now that the opposite is more likely to be rewarded: out of 18 eventually-published papers, I only managed to piss off the referees enough for a revise/resubmit decision once, and I really went out of my way to keep the proofs vague that time.

Of course, I had a largely unremarkable career in a somewhat niche subfield: I'm sure there are levels where (a), (b), and more importantly the sheer speed required to get a result out are bigger incentives. And from yet other fields, I occasionally hear rumors of people who master the art of opaque writing and "parallel construction" only to make it difficult for others to get ahead of them (hi שַשֶׁ!).

My advice to all academics in STEM is, just write the main body of the paper exactly as how the orthodoxy demands. Use the style needed to get the paper accepted. Then, add a supplementary or appendix of the paper that is written for the human graduate student. Put in worked out examples, further details on the proof. Most times, it will just get through, and you will have accomplished your goal.

If the journal demands you remove the appendix or supplementary, just remove it from the published manuscript. Then add it to your ArXiv submission.

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 presentations of the proofs as opaque as possible. You can see this in conference and workshop talks (which tend to happen pre-publication in math), in many fields speakers always avoid presenting _any_ proofs. Putting better explanations in an appendix, which the referees can read, simply wouldn't help.

2. Being easy-to-understand at first is actively punished, but even being easy-to-understand in the long run is not rewarded. You can always write an explanatory blog post after the publication decision has been made, but you won't put effort into writing one if you don't gain anything from it. This applies even more to the people in the example, who wrote on a typewriter in the 1970s. There were no blogs, and it was much harder to get an appendix through because page limits were physical limits, and the act of writing was much more onerous before the age of computers and LaTeX. There was no point to doing it given that it was actively discouraged.

I think this is fair criticism. I am coming for theoretical physics, where, at least in my area, I see my proposed strategy actually being practiced quite often. Physicists are quite a lot less grouchy than mathematicians, and there is a lot less of your point 1 in Physics.

That said, to present in "high impact" journals, you do have to write your results in some grand fashion where it is the greatest thing since sliced bread. But the results, not the proofs. Then again, the difficult theorem proving papers are rarely published in high impact journals.

Also, I have seen quite a number of papers where the arxiv submission is more updated/expanded than the published version. If you have some new framework that you want people to adopt, then it is in your benefit that grad students actually understand the ins and outs of it, so people so inclined do put in some effort to make their results accessible.

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?

Academics (not just mathematicians) are famously bitter and political, because they do things tht the world values so little, but they care about so much, and they are fighting for scraps of recognition and funding.

> 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 trivial anyway. Thankfully I remembered the exact place where the founder of the entire field had said just recently this is one of the hardest problems in the space and the problem he had hoped to maybe one day get to when he started the entire enterprise. The audience laughed and the guy apologized.

But I learned my lesson. Talks and papers need a little magic. For some people you can't just solve a cool problem, they need to think that they couldn't have done so and that they don't quite get how you did it. I now include something in every talk that I don't expect the audience to get just so what I'm doing seems "hard" to people who think this way.

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.

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.

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"

This is the HN IQ bias: assuming that smart people are somehow less susceptible to cognitive biases etc. that the mere mortals have.[1]

Smart people can be incredibly biased and ideological. Some careers for smart people are even all about reasoning backwards from a given conclusion.

[1] redacted footnote

> ... some terse typewritten notice from the 70s

Personally, I rather like these these; they have a certain retro-appeal, in particular old Springer mathematics publications. We are so spoilt with LaTex.

While gatekeeping is definitely a thing, I really suspect it's not the major incentive here.

In writing (both prose and code!) there is always a question of target audience, which inevitably excludes the not-target audience. Personally, for a field in which I'm an expert, it's really annoying to continually wade through introductory material and hand-holding just to get to some small nugget of substance. In that case, I'm definitely not the target audience, so I'll go looking for another communications channel that offers the compressed/elegant/general/abstract/terse formulations I desire. Please don't then insist that I'm being unfair and exclusionary if you're not the target audience on those specific communications channels.

For math papers and whatnot, whitepapers are like the one established channel for experts, while everyone else has textbooks, introductory pamphlets, blogs, youtube videos, etc. I agree, however, that there are cases where non-experts could benefit from knowledge siloed within expert communication channels, but this is an unfortunate systematic side-effect not malice.

Honestly, with software development, I find it disappointing that our social conventions currently conflate "readability" with "comfort and familiarity to Generic Programmer" instead of something more useful like "facilitates domain understanding and insight to the primary developers".

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. Personally, I think a reasonable bar is something like: a third-year PhD student in your broad area should be able to skim the paper and say a couple of paragraphs about what's happening and why it matters, and upon reading the paper more closely, present it in a seminar and defend it at least a couple of questions deep. IMO, most papers are not at this level, and are instead pitched at actual experts.

I think my point (and TFA's point as well) is that going from an experts-only paper to a seminar-ready one is actually not a ton of text. It might increase a paper's length by 5%. It's not about making everything longer, but adding enough context and signposting that the story can be followed at multiple levels, from the 5-minute pitch you'd get at a poster session to the every-detail one the author has. So I think we can have a paper that both the grad students and experts like.

I think doing this takes some skill and effort, which is well within the reach of most of the people who can write these papers, but way less effort is expended on this non-technical aspect.

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 19th century to just a year or two ago. In my experience, the older papers tend to be more understandable at a conceptual level but more modern ones tend to be more precise with the details. There is likely some survivorship bias here, though, as there has been more time for the worst of the old papers to be forgotten.

The writing style has also changed a lot— The older papers present things in a much more narrative way, and it can be a challenge to bring the kind of motivational context that allows into a paper that would feel at home in a modern publication.

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

Are these shared / mentioned anywhere?

A resource like this would be super helpful.

I would also be interested in reading some of these examples!

> Honestly, with software development, I find it disappointing that our social conventions currently conflate "readability" with "comfort and familiarity to Generic Programmer" instead of something more useful like "facilitates domain understanding and insight to the primary developers".

It's sort of a similar effect: most software is written by software people for other software people, just like most math is written by math people for other math people.

I personally have had the experience more than once of a mathematician apologizing for their code style but then handing me code that I find to be more straightforward and readable than usual.

What specific conventions do you think would facilitate domain understanding and insight?

I think it's the influence of Bourbaki[1] who were the original mathematical edgelords. I have a book (Creating Symmetry[2]) that explicits rejects this style. It's a lovely book.

[1]: https://en.wikipedia.org/wiki/Nicolas_Bourbaki

[2]: https://press.princeton.edu/books/hardcover/9780691161730/cr...

>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.

That seems like exactly the thing you want, if you are searching for a particular piece of information, the typesetting aside.

Especially the generality is important if you actually care about the result.

Terse statements are easier to prove.

>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.

Because it's an expository paper, not a reference manual. Applications help communicate and create understanding.

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.

> 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...

That's generally referred to as a Prisoner's Dilemma situation, where locally the incentives are to do something that makes it worse for everyone. The SlateStarCodex author generalized the concept into Moloch:

https://slatestarcodex.com/2014/07/30/meditations-on-moloch/

While I don't think it's practical to expect every paper author to write in the most consise and elegant style possible, one thing I do wonder is the lack of a "comment section" for papers: why isn't there a centralized place for academics to just leave comments or their understanding of the paper, like most of the web forums? I don't expect the author to respond or even be active in every comment section but there should certainly be such a place. Every other form of Internet-based discussion, including Reddit, any random Internet forum, mail lists, Discord, etc. are all interactive and everyone is expected to participate in a centralized and public discussion.

This way, even if the paper itself is hard to read, for the good ones I do expect someone else to leave a comment with a sketch of the most interesting parts of the paper that would get upvoted to the top, and the author could click a "promote" button or something to make it official. This way the author doesn't have to write very well as long as the paper is valuable enough for someone else to be interested.

Any comments section would require moderation, and internet moderation is a huge pain in the butt. It's not an unsolvable problem, as the examples you give demonstrate, but it does require a lot of effort, and I think you'd be pretty hard-pressed to find academics willing to expend that effort.