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 responses are some combination of
a) being concise and being elegant are the same, same for maximum generality/abstraction
b) the people who should read the paper don't need things explained
c) I am afraid that some smart egotistical professor whose opinion I value for some reason will call me soft if I add extra handholding material
(Nobody has ever really said c, but my sense is it's true. Academic writing has a lot of imitation of style to prove you're part of the in-group.)
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".
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.
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 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.
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.
Personally, I rather like these these; they have a certain retro-appeal, in particular old Springer mathematics publications. We are so spoilt with LaTex.
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...
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.
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. Let me give you a paragraph to give you the outline so that you can fill in the details yourself, rather than having to read all of the details just to reconstruct the outline."
I do have a pet peeve about mathematical exposition. At some point, phrases like "obviously" and "it is easy to see" became verboten, or at the very least frowned upon. The problem is that it didn't become verboten to skip details (this would be impossible in general), and those phrases actually do contain information. Namely they contain the information that there actually is some detail remaining to fill in here. Often in papers there will be some missing detail which is not so hard to verify, but whose presence is so ghostly in the exposition that I think I've missed somewhere where it was stated explicitly, and have to go back. I feel like this is the case of someone excising an instance of "it is easy to see that" and replacing it with... nothing.
> Not necessarily motivation in the sense of "why is this important", but motivation in the sense of "we are beginning a three page proof. Let me give you a paragraph to give you the outline so that you can fill in the details yourself, rather than having to read all of the details just to reconstruct the outline."
In graduate school this was the most frustrating aspect of paper reading (and writing). It makes sense why it exists however. Papers on mathematics in particular are laser targeted to a particular niche. As the science progresses you need more and more bespoke knowledge of previous work to even start the paper you're reading. There's an implicit assumption you've done your homework, so to speak, and authors likely feel there is no need to provide such a summary. Since, of course, if you don't have the pre-requisite knowledge the paper isn't targeted at you anyway.
Some of it of course is simply a pride thing. There have been many times I've felt the lack of exposition was a way to say "I'm better than you". I have no evidence this is the case but it would not surprise me.
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
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 context. It could make up the context but a good one would look up and offer an anecdote from Riemann's life or something. I see nothing wrong with that.
And LLM B could take a paper with that stuff, which to me is fluff, and strip it all out, leaving the dry bones for me to pick over and savour.
It would really just be another form of language translation, if a higher level one.
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 necessarily follow all the math. It just flows inordinately better than most modern papers - most of which are written on comparably simple and evolutionary (rather than revolutionary) topics.
Of course this may be an issue of domain. I'm mostly interested in cosmology/astronomy/physics, where math is a tool rather than the object of the paper itself.
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.
> 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.
> 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.
I think John Baez agrees with you. At the conclusion he says,
> The ideas here take practice to implement well, and they should not be overdone. I’m certainly not saying that a good math paper should remind readers of a story. Ideally the tricks I’m suggesting here will be almost invisible, affecting readers in a subliminal way: they will merely feel that that paper is interesting, carrying them in a natural flow from the title to the conclusion.
I would say "story mode" in papers is like dancing about your doctorate: really cool when the combination works, but the latter is where all the value lies, so it shouldn't sacrifice anything for the former.
What about LLM C, which takes a set of papers as vertices, forms an abstract simplex of all their combinations, and then spits out new papers on the ten most interesting higher-dimensional faces?
The best math book I've ever read -- which I think can completely transform somebody's appreciation of math -- was William Dunham's "Journey Through Genius - The Great Theorems of Mathematics."
What this book did was place mathematics in human and historical context. It starts with Hippocrates' Quadrature of the Lune, then moves on to Euclid's proof of the Pythagorean theorem, and moves along through history all the way down to Euler and Cantor.
I've always thought that the book's format or method is the best way to teach mathematics in a general sense. It beats the rote practice of formulae out of context, and it simultaneously teaches the history of mathematics and science. I'm always gifting parents of school-age children copies of this book.
Absolutely my favorite pop-sci/pop-math book of all time, if you can call it that.
That's because it's the only book I know which is in a good sweet spot between being a true pop-math book, giving the history and context of math (kind of like, say, Fermat's Enigma by Simon Singh), but while also being a real math book, and actually teaching real maths and real proofs of all the theorems talked about. There are some similar books, but most don't get the mix right, and even the ones that do, are just not as good.
Such a wonderful wonderful book. Do you have any other recommendations for similar books?
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.
Regarding you last point: out of interest, what kind of venues were you thinking of? Be this personal blogs of said academics, just dumping it on a preprint server or actual ("formally published") publications?
> 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.
> Of the people who see your math paper, 90% will only read the title. Of those who read on, 90% will only read the abstract. Of those who go still further, 90% will read only the introduction, and then quit.
My personal experience is usually quite different. Perhaps i'm very weird but i like to think i'm nothing special. I mostly read papers when searching for something specific (referral by someone in a discussion, searching for a definition, a proof). I almost never read the introductions, at least not in my first pass. My first pass is usually scanning the outline to search which section will contain what i'm searching for and then reading that, jumping back and forth between definitions and theorems. I usually then read discussion/related work at the end, to read about what the authors think about their method, what they like or dislike in related papers.
Abstract and introduction i only read when i have done several such passes on a paper and i realize i am really interested in the thing and need to understand all the details.
I very much hate this "be catchy at the beginning" and its extremist instantiation "the quest for reader engagement". Sure you should pay attention to your prose and the story you're telling. But treating reader of a scientific paper as some busy consumer you should captivate is just disrespectful, scientifically unethical and probably just coping with current organizational problems (proliferation of papers, dilution of results, time pressure on reviewers and researchers). Scientific literature is technical, its quality should be measured by clarity and precision, ease of searching, ease of generalization, honesty about tradeoffs. Not by some engagement metric of a damned abstract.
So, marketing is inevitable and necessary, but I have a hypothesis that the current Internet is making it worse. For example, creators (I'm lumping in researchers with songwriters, actors, etc) used to focus on passing the hurdle of getting an "elite" power (record company, publisher, University) to support them. Once over that hurdle, they specialized in creating and left marketing to the elite.
The elites would pressure the creators to do things they thought were marketable, but it didn't always work because creators had some leverage in negotiation and a small number of elites actually cared about making good stuff.
Now, there are fewer gatekeepers, but instead there is an all powerful algorithm. Creators all have to do their own marketing in addition to creating, and the algorithm can't be negotiated with.
So what we wind up with is insipid YouTube thumbnails and myriad academic papers with breathless "state of the art" claims.
There are tradeoffs, but I do think it's worth noticing how effectively we've started to reward creators for marketing rather than creating.
I remember once reading an opinion piece that suggested that most papers should trim the "introduction" section greatly, instead referring to key review papers or textbook entries. Although I've never followed this advice -- I want papers to be accepted, after all -- I can see a lot of merit to it.
The idea is to point readers to cohesive and well-cited treatments of the foundational material, rather than presenting them with a half-hearted pro forma summary that is unlikely to be especially insightful.
Fields that follow this scheme would likely accumulate some useful review papers that will actually be read, unlike the throw-away citations that appear in conventional introductions.
Would this scheme be beneficial to readers? I think so.
But will it take off? This seems unlikely. I read this opinion piece perhaps a decade or two ago, and I've not noticed a change in academic writing. If anything, the reverse has been true: I see more and more introductions that basically rehash introductions from other papers. And with LLM tools, this will only get worse ... the further the introduction is from the author's actual research interest, the higher the likelihood of it being irrelevant, puffed-up, or simply wrong.
I frequently have to read math/cryptography papers as part of my research, but I'm neither a mathematician nor a cryptographer, which makes things a bit of a slog.
I think this is mostly just down to me not being the target audience, but so many papers seem to be more of a "proof that the author understood this thing", rather than an attempt to actually convey that understanding.
It reminds me of when programmers needlessly optimize or "golf" their code - yes, very clever, but now I can't understand what it does.
Relevant, one of Simon Peyton-Jones's claims to fame is that he was too busy researching and publishing world-class research with world-class writing and teaching, that he didn't get a PhD.
I feel like this entire comment section grossly misunderstands what the author means with "story-mode". It's not about actually making anything read like fiction, just the order things are introduced to the reader.
"We lecturers naturally worry about the content of our lectures rather than the emotions we express in giving them. As human beings, students respond immediately to the emotive charge, even if they do not understand the content. The lecturer may have tried to give a balanced account of the debate between X and Y, but his preference for Y shines through. When the students come to write the essay on the relative merits of X and Y, they know where to put their money. The lecturer might try to balance the lecture by suppressing his enthusiasm for Y, but this ‗objective‘ presentation will make a mystery of the whole exercise. The students will wonder why they have to sit through all this stuff about X and Y when even the lecturer does not seem to care much for either of them. The better strategy is for the lecturer to plunge into the works of X, reconstruct X‘s mental world and re-enact X‘s thoughts until he shares some of X‘s intellectual passions. We can be sure that X had intellectual passions, else we would not now have the works of X."
Was initially expecting this to be more “elementary education” focused rather than academic math.
Good article. As a non-academic, it is cool to see the idea of “what makes a good paper” explored.
A lot of the concepts mentioned seem to hold up really well in theory but ultimately just seem like stylistic differences, to me.
Academic writing can have an international audience and perhaps “just being technical” has advantages.
That doesn’t change the point of the article, though.
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.
> 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.
Perhaps I'm the wrong type of human, but this still does not resonate at all.
Stephen Leacock answered this topic perfectly over a hundred years ago in Moonbeams from the Larger Lunacy, chapter six, Education Made Agreeable or the Diversions of a Professor.
Minor excerpts to whet your appetite (but seriously, read it, it’s excellent humour):
> In the first place I have compounded a blend of modern poetry and mathematics, which retains all the romance of the latter and loses none of the dry accuracy of the former. Here is an example:
The poem of
LORD ULLIN’S DAUGHTER
expressed as
A PROBLEM IN TRIGONOMETRY
…
—⁂—
> Here, for example, you have Euclid writing in a perfectly prosaic way all in small type such an item as the following:
> “A perpendicular is let fall on a line BC so as to bisect it at the point C etc., etc.,” just as if it were the most ordinary occurrence in the world. Every newspaper man will see at once that it ought to be set up thus:
AWFUL CATASTROPHE
PERPENDICULAR FALLS HEADLONG
ON A GIVEN POINT
The Line at C said to be completely bisected
President of the Line makes Statement
etc., etc., etc.
It's not just papers. I tried to learn probabilities theory & statistics, deeper than little knowledge I kept from the uni. For instance, wanted to understand how you solve problems like samples in quality control: if in a sample of N items, m are bad, what's the chance X% are bad in production?
Unfortunately, there are either introductory materials (toss a coin -- 50% chance faces) or some robot language. Or schizophrenic: like starting from the middle of a speech.
I feel like you must be a using a wrong approach to searching for mathematics.
In your case I would search for a script or book with title "Introduction to probabilify theory" or "Introduction to mathematical statistics". Then you skim through it to see if you can find an analysis of your problem. If not, you can hopefully find out what the right keywords are to then find a more advanced script or book for the specific subfield your problem needs.
Decades ago, I struggled with the start of a math class as a young engineering student until one professor, one day, said, "It's easy to calculate how many feet of steel you need to get from point A to point B but what if you need to calculate the number of feet for the curved support under the Eads' bridge?" He then proceeded to show how it's done and everything sunk in after that.
[+] [-] mycologos|2 years ago|reply
I have talked with math people about why this is, and responses are some combination of
a) being concise and being elegant are the same, same for maximum generality/abstraction
b) the people who should read the paper don't need things explained
c) I am afraid that some smart egotistical professor whose opinion I value for some reason will call me soft if I add extra handholding material
(Nobody has ever really said c, but my sense is it's true. Academic writing has a lot of imitation of style to prove you're part of the in-group.)
[+] [-] xelxebar|2 years ago|reply
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".
[+] [-] noelwelsh|2 years ago|reply
[1]: https://en.wikipedia.org/wiki/Nicolas_Bourbaki
[2]: https://press.princeton.edu/books/hardcover/9780691161730/cr...
[+] [-] saithound|2 years ago|reply
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!).
[+] [-] humansareok1|2 years ago|reply
Outside of Applied Math why would this be an expectation at all?
[+] [-] constantcrying|2 years ago|reply
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.
[+] [-] renonce|2 years ago|reply
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.
[+] [-] mayd|2 years ago|reply
Personally, I rather like these these; they have a certain retro-appeal, in particular old Springer mathematics publications. We are so spoilt with LaTex.
[+] [-] araes|2 years ago|reply
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...
[+] [-] Sirizarry|2 years ago|reply
[+] [-] sublinear|2 years ago|reply
[+] [-] bigbacaloa|1 year ago|reply
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[+] [-] woopwoop|2 years ago|reply
I do have a pet peeve about mathematical exposition. At some point, phrases like "obviously" and "it is easy to see" became verboten, or at the very least frowned upon. The problem is that it didn't become verboten to skip details (this would be impossible in general), and those phrases actually do contain information. Namely they contain the information that there actually is some detail remaining to fill in here. Often in papers there will be some missing detail which is not so hard to verify, but whose presence is so ghostly in the exposition that I think I've missed somewhere where it was stated explicitly, and have to go back. I feel like this is the case of someone excising an instance of "it is easy to see that" and replacing it with... nothing.
[+] [-] zer8k|2 years ago|reply
In graduate school this was the most frustrating aspect of paper reading (and writing). It makes sense why it exists however. Papers on mathematics in particular are laser targeted to a particular niche. As the science progresses you need more and more bespoke knowledge of previous work to even start the paper you're reading. There's an implicit assumption you've done your homework, so to speak, and authors likely feel there is no need to provide such a summary. Since, of course, if you don't have the pre-requisite knowledge the paper isn't targeted at you anyway.
Some of it of course is simply a pride thing. There have been many times I've felt the lack of exposition was a way to say "I'm better than you". I have no evidence this is the case but it would not surprise me.
[+] [-] igorbark|2 years ago|reply
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
[+] [-] gumby|2 years ago|reply
But (not joking here) this is a perfect opportunity for an LLM -- two opportunities, actually.
LLM A takes a dry paper and gives it context. It could make up the context but a good one would look up and offer an anecdote from Riemann's life or something. I see nothing wrong with that.
And LLM B could take a paper with that stuff, which to me is fluff, and strip it all out, leaving the dry bones for me to pick over and savour.
It would really just be another form of language translation, if a higher level one.
[+] [-] somenameforme|2 years ago|reply
Of course this may be an issue of domain. I'm mostly interested in cosmology/astronomy/physics, where math is a tool rather than the object of the paper itself.
[1] - https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf
[+] [-] gravescale|2 years ago|reply
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.
[+] [-] darby_eight|2 years ago|reply
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.
[+] [-] nextaccountic|2 years ago|reply
I think John Baez agrees with you. At the conclusion he says,
> The ideas here take practice to implement well, and they should not be overdone. I’m certainly not saying that a good math paper should remind readers of a story. Ideally the tricks I’m suggesting here will be almost invisible, affecting readers in a subliminal way: they will merely feel that that paper is interesting, carrying them in a natural flow from the title to the conclusion.
[+] [-] 082349872349872|2 years ago|reply
What about LLM C, which takes a set of papers as vertices, forms an abstract simplex of all their combinations, and then spits out new papers on the ten most interesting higher-dimensional faces?
[+] [-] A_D_E_P_T|2 years ago|reply
What this book did was place mathematics in human and historical context. It starts with Hippocrates' Quadrature of the Lune, then moves on to Euclid's proof of the Pythagorean theorem, and moves along through history all the way down to Euler and Cantor.
I've always thought that the book's format or method is the best way to teach mathematics in a general sense. It beats the rote practice of formulae out of context, and it simultaneously teaches the history of mathematics and science. I'm always gifting parents of school-age children copies of this book.
[+] [-] edanm|2 years ago|reply
That's because it's the only book I know which is in a good sweet spot between being a true pop-math book, giving the history and context of math (kind of like, say, Fermat's Enigma by Simon Singh), but while also being a real math book, and actually teaching real maths and real proofs of all the theorems talked about. There are some similar books, but most don't get the mix right, and even the ones that do, are just not as good.
Such a wonderful wonderful book. Do you have any other recommendations for similar books?
[+] [-] gthrow12345|2 years ago|reply
[+] [-] kouru225|2 years ago|reply
[+] [-] mayd|2 years ago|reply
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 places to publish nontechnical academic writing.
[+] [-] Ekaros|2 years ago|reply
[+] [-] sweezyjeezy|2 years ago|reply
Not the biggest issue in maths - the arxiv version usually won't match the journal version 1:1
[+] [-] jcla1|2 years ago|reply
[+] [-] lupire|2 years ago|reply
[+] [-] Ar-Curunir|2 years ago|reply
Well thank god we have preprint servers which have no such stupid requirements.
[+] [-] twelfthnight|2 years ago|reply
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.
[+] [-] Brian_K_White|2 years ago|reply
https://maa.org/sites/default/files/pdf/devlin/LockhartsLame...
It makes a very different point about teaching, or learning/discovering math, not writing about math.
[+] [-] kouru225|2 years ago|reply
[+] [-] lapinot|2 years ago|reply
My personal experience is usually quite different. Perhaps i'm very weird but i like to think i'm nothing special. I mostly read papers when searching for something specific (referral by someone in a discussion, searching for a definition, a proof). I almost never read the introductions, at least not in my first pass. My first pass is usually scanning the outline to search which section will contain what i'm searching for and then reading that, jumping back and forth between definitions and theorems. I usually then read discussion/related work at the end, to read about what the authors think about their method, what they like or dislike in related papers.
Abstract and introduction i only read when i have done several such passes on a paper and i realize i am really interested in the thing and need to understand all the details.
I very much hate this "be catchy at the beginning" and its extremist instantiation "the quest for reader engagement". Sure you should pay attention to your prose and the story you're telling. But treating reader of a scientific paper as some busy consumer you should captivate is just disrespectful, scientifically unethical and probably just coping with current organizational problems (proliferation of papers, dilution of results, time pressure on reviewers and researchers). Scientific literature is technical, its quality should be measured by clarity and precision, ease of searching, ease of generalization, honesty about tradeoffs. Not by some engagement metric of a damned abstract.
[+] [-] twelfthnight|2 years ago|reply
The elites would pressure the creators to do things they thought were marketable, but it didn't always work because creators had some leverage in negotiation and a small number of elites actually cared about making good stuff.
Now, there are fewer gatekeepers, but instead there is an all powerful algorithm. Creators all have to do their own marketing in addition to creating, and the algorithm can't be negotiated with.
So what we wind up with is insipid YouTube thumbnails and myriad academic papers with breathless "state of the art" claims.
There are tradeoffs, but I do think it's worth noticing how effectively we've started to reward creators for marketing rather than creating.
[+] [-] bluenose69|2 years ago|reply
The idea is to point readers to cohesive and well-cited treatments of the foundational material, rather than presenting them with a half-hearted pro forma summary that is unlikely to be especially insightful.
Fields that follow this scheme would likely accumulate some useful review papers that will actually be read, unlike the throw-away citations that appear in conventional introductions.
Would this scheme be beneficial to readers? I think so.
But will it take off? This seems unlikely. I read this opinion piece perhaps a decade or two ago, and I've not noticed a change in academic writing. If anything, the reverse has been true: I see more and more introductions that basically rehash introductions from other papers. And with LLM tools, this will only get worse ... the further the introduction is from the author's actual research interest, the higher the likelihood of it being irrelevant, puffed-up, or simply wrong.
[+] [-] Retr0id|2 years ago|reply
I think this is mostly just down to me not being the target audience, but so many papers seem to be more of a "proof that the author understood this thing", rather than an attempt to actually convey that understanding.
It reminds me of when programmers needlessly optimize or "golf" their code - yes, very clever, but now I can't understand what it does.
[+] [-] gbacon|2 years ago|reply
Related gems from Simon Peyton Jones are below. In the first, he also advocates telling a story.
https://www.microsoft.com/en-us/research/uploads/prod/2016/0...
https://www.microsoft.com/en-us/research/uploads/prod/2016/0...
https://simon.peytonjones.org/assets/pdfs/writing-a-proposal...
[+] [-] lupire|2 years ago|reply
[+] [-] Warwolt|2 years ago|reply
[+] [-] zogrodea|2 years ago|reply
https://uhra.herts.ac.uk/bitstream/handle/2299/5831/903260.p...
"We lecturers naturally worry about the content of our lectures rather than the emotions we express in giving them. As human beings, students respond immediately to the emotive charge, even if they do not understand the content. The lecturer may have tried to give a balanced account of the debate between X and Y, but his preference for Y shines through. When the students come to write the essay on the relative merits of X and Y, they know where to put their money. The lecturer might try to balance the lecture by suppressing his enthusiasm for Y, but this ‗objective‘ presentation will make a mystery of the whole exercise. The students will wonder why they have to sit through all this stuff about X and Y when even the lecturer does not seem to care much for either of them. The better strategy is for the lecturer to plunge into the works of X, reconstruct X‘s mental world and re-enact X‘s thoughts until he shares some of X‘s intellectual passions. We can be sure that X had intellectual passions, else we would not now have the works of X."
[+] [-] dieselgate|2 years ago|reply
[+] [-] shadowgovt|2 years ago|reply
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.
[+] [-] Tutitk|2 years ago|reply
Over time it will probably grow into long-long editorial pieces. I will propably have to use AI to strip down the story mode.
[+] [-] jimmar|2 years ago|reply
> 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.
Perhaps I'm the wrong type of human, but this still does not resonate at all.
[+] [-] chrismorgan|2 years ago|reply
https://www.gutenberg.org/files/4064/4064-h/4064-h.htm#link2...
Minor excerpts to whet your appetite (but seriously, read it, it’s excellent humour):
> In the first place I have compounded a blend of modern poetry and mathematics, which retains all the romance of the latter and loses none of the dry accuracy of the former. Here is an example:
…—⁂—
> Here, for example, you have Euclid writing in a perfectly prosaic way all in small type such an item as the following:
> “A perpendicular is let fall on a line BC so as to bisect it at the point C etc., etc.,” just as if it were the most ordinary occurrence in the world. Every newspaper man will see at once that it ought to be set up thus:
[+] [-] culebron21|2 years ago|reply
Unfortunately, there are either introductory materials (toss a coin -- 50% chance faces) or some robot language. Or schizophrenic: like starting from the middle of a speech.
[+] [-] golol|2 years ago|reply
[+] [-] assimpleaspossi|2 years ago|reply