19 ms·

Math writing is dull when it neglects the human dimension

223 points by mathgenius 3y ago

bedobi 3y ago
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 the distance to and size of the moon with trigonometry I was floored. Oh ok so that’s the kind of cool shit they came up with it for. Now I’m listening.
- loloquwowndueo 3y ago
  Sounds like you had crappy teachers.
  - latency-guy2 3y ago
    Establish why its "crappy teacher" and not "crappy student". I've seen far more of the latter than the former. I don't think its hard to find something interesting about math either, and it is immediately applicable, even with what I think is extremely stupid in the form of common core as presented in the USA, you are literally being presented story problems about common every day occurrences and activities.
    - atoav 3y ago
      As someone who routinely teaches (Non-STEM) university students practical applications of math I can assure you that none of the students that told me "I am bad at maths" went out of my class without an understanding of the topics we talked about. Yet I routinely hear a: "Wow, if they told it to me this way during school I might have cared!" or "It really made my head smoke, but it felt good." Step 1 is believing that every person that doesn't have cognitive problems can understand an abstract concept if it is explained well and they got the motivation to understand it. Then you need to create a situation which motivates them to understand it and now you only need to explain it well. Many math teachers fail already at step 1. They believe 90% of their students are too stupid to understand things, while this is just a convinient explaination for their own failures. I once was convinced of being that student. I met one kid that I couldn't teach anything because he would forget things I told him 15 minutes befoee. He was a refugee from Afghanistan and severely traumatized. The truth is that we should look to the best when teaching and we would be stupid if we didn't. And the best are people like 3blue1brown. If your class falls significantly below such a level of clarity and engagement it will suck. During my own math education I had teachers that left out the most fundamental applications. E.g. something like an integral has clear applications, it is a new super power with which you can solve new problems — yet all we did was learning a receipe and solving abstract problems. The fact that it was a super power was something I had to figure out myself, later. And this was common. I even was lucky because I had a good physics teacher who managed to being up a lot of what we learned in math and give it a more practical feel, but most of my friends from other schools were not so lucky.
      - bedobi 3y ago
        This is exactly how my education went. Oh you're not engaged with my shitty teaching and forcing you to do endless abstract nonsensical formulae with zero contextualization or application? Then you're the problem - you have cognitive defects, you are plain dumb and stupid, you are disinterested, you don't care about your education etc etc so I cannot help you. Now let me spend my time on "teaching" the kids who mostly already know what I'm "teaching".
        latency-guy2 3y ago
        > This is exactly how my education went. No it didn't. I am very confident it did not. All students that make it past grade school go through nearly the exact same sequence and motivating examples beginning from geometry, high school algebra, and then some introduction to calculus if not calculus outright. And the motivating example has always been how to calculate area, and if advanced enough, volume, for all kinds of shapes, regular or otherwise. This is not a recent development, its been the motivating example and the entire purpose for calculus having been invented. I am so confident in this that I am here to call you a terrible student and that, yes, you likely were a terrible student, especially since your characterization is the exact standard excuse I hear from terrible students. So now I have to drill - what was "nonsensical"? What had "zero context"? You immediately have lost the claim of "zero application", so we don't have to go there. If your claim is beyond K-12 math and into university, then I would be too upset to even argue with you if that is your actual position. Making these claims after more than a decade of learning math tells me you have trained yourself to forget all you learned.
        atoav 3y ago
        Interesting form of confidence. I didn't write the comment you replied to, but I wrote the original comment. The first fact I want to have written down is that there are bad math teachers. And sadly it is not uncommon for them to be bad, as I mentioned most of my collegues from other classes and schools had bad math teachers and some of them were people that liked math. Now as an educator I am aware that students are quick to blame other people or the system for their own deficiencies, but I can tell you for a fact that our math teacher failed to explain us what an integral was actually for in an parsable way, even after multiple times of asking. She just knew how to do the formula stuff, she never used it herself on real applications. And when she did explain things, she always did it once, much too briefly in the beginning, so that by the point at which we started doing her always decidedly abstract examples nobody knew what the fuck this was for. As I said, our physics and mechanica teachers were better math teachers than her. As for the integral I had to go and look it up myself, the internet was still young and there weren't many grown ups who knew how to look such a thing up and when I saw the explainations I wondered why nobody ever told us..? I understand btw. why it can be an advantage to understand math in purely abstract ways, but in her case she just didn't want to talk much and stick to the examples. And that is bad teaching. Ah and before we get into a discussion about specifics, like many on this site I grew up and live happily outside of the US, so educational plans etc. might differ.
- pylua 3y ago
  That is a consistent problem with the education system no matter what the topic is with few exceptions.
  - mycologos 3y ago
    I think the economic returns to "decent understanding of X plus decent communication skills" are much higher when X is math than when X is art or language or history, so you need a greater passion for teaching to select it in spite of that fact, and this shrinks the pool of good math teachers relative to other subjects.
  - bobajeff 3y ago
    I'm pretty sure math is the most poorly taught subject out of all of them. Social studies, current events, history, literature arts are mostly skills most people use everyday. Math is important so every school is required to teach it however not many schools can. The issue with math is there are never going to be very many good math teachers as that would require many more people who know math. How many adults even know math beyond basic arithmetic?
    - melagonster 3y ago
      Even the basic content from textbook is not real mathematics. the daily work of mathematician is very different to calculate some interesting things.
- melondonkey 3y ago
  Hard to meet everyone where they are and at the same time give them a relevant practical application for their own life. Good learners just soak it up and look for the application later. But that also doesn’t fit all. It’s hard to even write a pop song that everyone likes so math education that appeals to all is almost impossible
- skhunted 3y ago
  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.
  - atoav 3y ago
    Haven't thought is for decades, but was my environments favourite math tutor, because I managed to ground everything in people's reality and rell them a compelling fiction in which knowing how to do the thing was actually a super-power. You know like the survival tricks certain preppers learn and never use — that, but with math. Even if the examples were sometimes over the top, involved flaming moats and other xkcd-like freakiness I got students where their teachers told me it is hopeless sitting there participating with glowing eyes. Meanwhile in my own math education I had a teacher who made us do integrals for what felt like a year without telling us once what the hell it is needed for. I had to figure that out on my own. My colleagues who didn't care just learned it by hard and forgot it immediately after. But I guess they got thought all the material and got ok grades so their education was a success. What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep.
    - skhunted 3y ago
      What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep. This is precisely what I was referring to about people who come back at a later time and relearn the stuff. They want applications. At the time a class is taken very few actually want to dive into applications. The subject has been taught the way it is taught for a reason.
- bawolff 3y ago
  > How did folks come up with and it, prove it works and start using it I mean, anything at the university level should include proofs on why it works. I would go as far as to say you aren't really doing math if there are no proofs.
  - lupire 3y ago
    elementary level too! Humans crave understanding. This is what we finally have with modern materials like Eureka.
- golol 3y ago
  Did you not have a physics class around the same time you learned calculus and linear algebra? That makes it obvious what the application is.
- constantcrying 3y ago
  This is completely asinine. What you say applies to every subject in school. I interpreted poetry, learned ancient history and dead language. Yet somehow the single most useful tool of thought humans have developed needs to justify itself so that you will learn it?
- eternityforest 3y ago
  I did a (not fully third party reviewed for errors, watch out) project to record all the math related "cool shit I'm glad to have discovered": https://github.com/EternityForest/AnyoneCanDoIt/blob/master/MathELI5.md https://github.com/EternityForest/AnyoneCanDoIt/blob/master/...
- jrm4 3y ago
  It's really this. I was a "good" student so I got pretty far in college math; and none of it has stuck with me without a real life application. At ALL. What's kind of killing me now, as my kids go through algebra et al, is that now we have a VERY OBVIOUS way to make this interesting and we're severely underutilizing it, which is video games. "Draw a rainbow in Minecraft" or "Figure out the trajectory of that frag grenade" seems just gobsmackingly obvious as a path here.
mycologos 3y ago
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.)
- saithound 3y ago
  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!).
  - abdullahkhalids 3y ago
    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.
Brian_K_White 3y ago
I always liked Lockhart's Lament https://maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf 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 3y ago
  Paul Lockhart was my high school teacher! He completely changed my mind about math.
daxfohl 3y ago
The same should be said for engineering design docs tbh
- serf 3y ago
  absolutely disagree. an engineering design document is about information retrieval, not education. It's not made to entertain or educate about new concepts, it's made to be terse and rigidly structured for the sake of aiding the work of the reader and to provide reliable information recall methods for those reading it. I don't want to know what 'problems are worth attacking' when reading a design document, I want to know what tolerance criteria the hole on the left flange needs to meet. There is more wiggle-room for artistic expression when we're talking about analytical papers like feasibility and failure analysis. It doesn't belong in the design phase. It creates confusion and ambiguity for the reader often, and those two things need not be introduced into design more than they already exist.
  - Jensson 3y ago
    > It's not made to entertain or educate about new concepts, it's made to be terse and rigidly structured for the sake of aiding the work of the reader and to provide reliable information recall methods for those reading it. That goes for math papers as well. Both needs to be understood by juniors, both are used by experts for lookup and work.
  - eternityforest 3y ago
    I might want to know why the hole on the left flange needs such insane tolerance though. Maybe it's not relevant in a specific version, or maybe I have an idea for how to solve the issue so it can be made cheaper, etc. Maybe it's absolutely integral to the whole application and I should stop wasting my time trying to make a printed PLA version, etc.
- constantcrying 3y ago
  Absolutely not. Engineering design docs should be terse and to the point. Documentation is not a medium where you want to tell a story, because that makes it instantly much less usable, since people will read it at random parts to attain specific information.
twelfthnight 3y ago
> 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.
- johncarlosbaez 3y ago
  Everything is always subliminally affecting you. It might as well do it in a helpful way.
  - twelfthnight 3y ago
    > everything is always subliminally affecting you Right, but certain methods are more effective than others. This paper is arguing and encouraging exactly how to manipulate more effectively. > It might as well do it in a helpful way Being more effective in teaching I agree is a good thing. But a math paper isn't for teaching, it's for showing a proof or making an argument. I just think we ought to set standards on academic research to remain as neutral as possible to let ideas flourish on merit rather than cunning tricks. EDIT: I get that a career in academia requires all these games to get more citations. Looks at ML research, I feel like abstracts are written by used car salesman nowadays. So like, if you have to do it do it. But we ought to call it out from time to time.
    - elbear 3y ago
      I think it was the word "subliminal" that made you think of manipulation. On the other hand, I read the quote you posted as meeting the reader at their level and guiding them to a clearer, deeper understanding by providing information in a logical, intuitive way. This would mean, for example, providing real-world context for each abstract concept introduced, rather than just leaving the concept by itself together with an abstract definition.
- ajkjk 3y ago
  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.
dieselgate 3y ago
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.
layman51 3y ago
This really reminds me of a writing course I took called “Writing Stories for Science”. That’s where I first encountered the idea of story beats. The class seemed more focused on the natural sciences and story structures, so I got the impression this must be very difficult to apply to pure mathematical writing. Maybe it’s easier in applied mathematics where there’s a clearer reason that could be explained to a layperson.
- hazbot 3y ago
  I don't think the point here is to make a math paper understandable to a lay person, but rather make it interesting and contextualize it for other academics.
  - 082349872349872 3y ago
    Other academics are already interested and either already have or know where to get the context; that's why the style is the way it is.
js8 3y ago
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 code), so that we could run the state machine on a computer and get a result. However, once you know what it takes to invert boolean functions, you don't need the solution step, you can just quantize your equation (problem) directly to a SAT instance, and let the inversion algorithm do all the hard work. No (elegant and readable) math is required anymore. So I think we better treat mathematics as a "useless" human artifact (like art or chess) rather than something of practical value.
- yau8edq12i 3y ago
  > 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 be able to give you a proof on demand on statement number 123456789 in some Gödel numbering of statements. What it won't be able to tell you is that the theorem should be called the "intermediate value theorem" and what it means. Math isn't just coming up with formally correct proofs for pre-existing statements. I also don't see what "P vs NP" has to do with anything. > 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 code), so that we could run the state machine on a computer and get a result. I'm a mathematician. What you wrote is just bonkers. Some parts of math are about writing algorithms to solve equations. The vast majority of math isn't.
  - js8 3y ago
    My point is, the need for semantics is a human construct, it's not required to solve practical problems. Practical value of MVT is that we can apply it in the process of describing a solution, i.e. an algorithm. But if you have a SAT algorithm that can somehow inherently apply a finite instance of MVT, you no longer need to know what MVT is. And this is at the heart of P vs NP question, how to solve SAT, and once we understand that, all the math that is about solving equations (i.e. that of practical value) will become very boring. Kinda like when a game becomes solved with a computer. (This reminds me of Chomsky and Norvig debate on the machine learning and nature of understanding. I wouldn't think I would take Norvig's position, yet here we are.) Addendum: I am also not arguing that computers writing proofs are a necessity for this, but rather efficiently (as possible) solving SAT instances. You don't need to state a hypothesis (and thus prove it) for an infinite number of cases to solve practical problems. I am also not judging value of math - yeah, it is fun. All I am saying it inherently has a human dimension in the sense we don't need it (assuming we have an efficient SAT solver) to solve practical problems.
culebron21 3y ago
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.
- golol 3y ago
  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.
  - culebron21 3y ago
    That's what I tried to avoid in the first place :)
    - KeplerBoy 3y ago
      But that's the entry point. Well written textbooks, which discuss the right problem are invaluable. If you head straight to google scholar, you're going to have a bad time.
    - constantcrying 3y ago
      So you tried to avoid an instructive text which is set up to allow readers to learn about the details of the subject starting from the ground up? And you are complaining that you can't find a resource which does exactly that?
      - culebron21 3y ago
gumby 3y ago
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.
- 082349872349872 3y ago
  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?
- somenameforme 3y ago
  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. [1] - https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf
  - Someone 3y ago
mayd 3y ago
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 places to publish nontechnical academic writing.
- sweezyjeezy 3y ago
  > Space in academic journals is too precious to waste on inessential content Not the biggest issue in maths - the arxiv version usually won't match the journal version 1:1
  - melagonster 3y ago
    and they publish on internet, solid copy is not popular today.
- jcla1 3y ago
  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?
- Ekaros 3y ago
  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.
- lupire 3y ago
  #5 being exclusionary to people with different/better ideas/practices is not an pillar worth preserving.
- Ar-Curunir 3y ago
  "Space in academic journals is precious" Well thank god we have preprint servers which have no such stupid requirements.
Tutitk 3y ago
The "dull" version is two times smaller and much easier to read. Hard pass for me. Over time it will probably grow into long-long editorial pieces. I will propably have to use AI to strip down the story mode.
seanhunter 3y ago
This is one of those things that is extremely insidious because it holds a kernel of truth but the author takes it to a place that in my opinion is really unhelpful. For example, his opening paragraph "One of the main problems..." seems fine to me for setting the context, but I would immediately want him to follow with "Let ..." and state the proper definition. All of the extra fluffiness means I have to do two translations - from the fluffy part to the actual maths and then back again - each time to understand what he is getting at. In my opinion, great maths writing is both rigourous and engaging. I would use "Calculus" by Michael Spivak as an example. It's really lovely to read but also concise and elegant and the beauty of (and love for) the maths comes through on every page. The author isn't trying to turn it into a short story and it's not padded out with additional rhetorical bullshit like "And now we come to a key player: the group of deck transformations." That sentence makes me want to puke just a little bit. But all of the above is a matter of opinion. This, for me is a hard nope: 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. I really really hate it when people do shit like this. State things properly even if you need to say something like "don't worry about x y z condition I put there for now which will be explained later". He says you must warn the reader you're doing this but basically I think this is just a hard pass from then onwards. Like if you want to give a simpler version of something, you can by all means do: This is known as seanhunter's theorem, which is usually stated as, if blah blah blah... When x is a real number greater than zero this can be simplified as follows: If x is the number of minutes spent in a meeting and p is the number of participants, then the expected value of the meeting is given by v= r/sqrt(x^3p^2) r~N(mu, sigma^2) ... or whatever. So you give the real version and then the "special case" version that is actually useful most of the time. Like when people give you Fermat's little theorem[1] and they say a^p is congruent with a mod p but that is equivalent to saying if p does not divide a then a^(p-1) congruent with 1 (which is the one you're going to actually use most of the time). [1] https://en.wikipedia.org/wiki/Fermat's_little_theorem https://en.wikipedia.org/wiki/Fermat's_little_theorem
assimpleaspossi 3y ago
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.
hcks 3y ago
No, not everything should be written in the style of a NYT best-seller non-fiction, actually
the_panopticon 3y ago
always a good read on mathematical writing https://www.mathematik.uni-marburg.de/~agricola/material/halmos.pdf https://www.mathematik.uni-marburg.de/~agricola/material/hal...
zogrodea 3y ago
Some ight appreciate the following short paper, relatedly. A quote is extracted below. https://uhra.herts.ac.uk/bitstream/handle/2299/5831/903260.pdf 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."
Retr0id 3y ago
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.
A_D_E_P_T 3y ago
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.
- kouru225 3y ago
  Putting it on my list
- gthrow12345 3y ago
  My college advisor gifted me a copy when I graduated, and I passed it along to one of the best students that I had. Great book.
- edanm 3y ago
  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?
lapinot 3y ago
> 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.
- twelfthnight 3y ago
  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.
bluenose69 3y ago
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.
- datascienced 3y ago
  If academic papers were published in HTML with living links on the web it would help. Hypertext solves this but are they not allowed to use modern (1990s+) technology?
  - lupire 3y ago
    URLs die. A good citation can be interpreted by technology to search and locate the referenced object.
    - datascienced 3y ago
      As the meme says: why not have both, or even an extension to HTML for a permanent reference that your browser can then resolve using the least defunkt current resolver.
queuebert 3y ago
This comment below the article from the author cracked me up: "Part of why this paper took so long to write is that the file was called boring.tex."
seba_dos1 3y ago
The entirety of math is "human", there's no way for it to neglect that "dimension". (the article's title is "Why Mathematics is Boring")
chrismorgan 3y ago
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. https://www.gutenberg.org/files/4064/4064-h/4064-h.htm#link2H_4_0020 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: 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.
thpl2k3j4324234 3y ago
[flagged]
- Ar-Curunir 3y ago
  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.
j2kun 3y ago
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.
- Ar-Curunir 3y ago
  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.
gbacon 3y ago
Thank you. This is beautiful. 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/2016/07/How-to-write-a-great-research-paper.pdf https://www.microsoft.com/en-us/research/uploads/prod/2016/0... https://www.microsoft.com/en-us/research/uploads/prod/2016/07/How-to-give-a-great-research-talk.pdf https://www.microsoft.com/en-us/research/uploads/prod/2016/0... https://simon.peytonjones.org/assets/pdfs/writing-a-proposal-mar23.pdf https://simon.peytonjones.org/assets/pdfs/writing-a-proposal...
- lupire 3y ago
  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.
woopwoop 3y ago
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.
- igorbark 3y ago
  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
  - samatman 3y ago
    Like everything in mathematics, "obvious" is a term of art. Broadly speaking, it refers to a fact, proof, consequence, which is necessary for the proof to advance, but which is already established elsewhere, so it does not in itself aid in understanding the proof being presented. A proof is either providing a new result, or is proving an established result in a new way. Almost always, a proof will need other results, in a way that isn't "interesting" (another term of art). The point of introducing these results as "obvious" is basically to say "here is something which isn't proven by the proof I'm presenting, we need it, but there's no need to derive it to follow this proof", ideally, with a footnote. As language, it is a bit sly: if something is obvious in the normal sense, it will be left out. It's a problem that the modern style is to elide anything obvious in this sense, rather than in the sense of "anyone who might reasonably read this paper may be expected to know this". But labeling these things as obvious isn't meant in the sense "if you don't know this, you're stupid or uninformed", or in fact "this will be instantly clear as soon as I mention it", it's meant to mean "if you were to follow the breadcrumbs and check up on the 'obvious' thing, it wouldn't help you much in following my proof, so take my word for it. Or, y'know, knock yourself out if this step is interesting to you".
Warwolt 3y ago
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.
jimmar 3y ago
This was the "good" example: > 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.
tombert 3y ago
I don't know what's objectively "correct", but my favorite CS papers are the ones that try and be more entertaining to read. Stuff like "Cheney on the MTA", or the "Lambda the Ultimate" papers are fun to read, while still dumping a lot of interesting information. I also think Lamports papers tend to be more fun simply because they use more tangible analogies for things rather than sticking with formalized mathematics. I kind of view the overly dry, super-formal math/CS papers to be almost a form of gatekeeping. There's a lot of really useful information in a lot of papers, but people don't read them because they rely on a lot of formalisms and notation that are pretty dry to learn about. Sure, I know what a "comonad" and "endofunctor" is, and using terms like that can be useful, but I also think that it can sometimes be better to take a simpler, more grounded approach to things, or at least work with metaphors.
ivanjermakov 3y ago
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.
- Ar-Curunir 3y ago
  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.
shadowgovt 3y ago
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.
amai 3y ago
It is a long and old tradition in math to explain your findings as obscure as possible to make sure that your competitors cannot follow you. "He is like the fox, who effaces his tracks in the sand with his tail" (Abel about Gauss) https://hsm.stackexchange.com/questions/3610/what-is-the-original-source-for-abels-quote-about-gausshe-is-like-the-fox-wh https://hsm.stackexchange.com/questions/3610/what-is-the-ori...
nso95 3y ago
It seems unreasonable to expect someone to both be an expert in mathematics as well be some great story teller

223 points by mathgenius 3y ago

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 the distance to and size of the moon with trigonometry I was floored. Oh ok so that’s the kind of cool shit they came up with it for. Now I’m listening.

loloquwowndueo 3y ago
Sounds like you had crappy teachers.
- latency-guy2 3y ago
  Establish why its "crappy teacher" and not "crappy student". I've seen far more of the latter than the former. I don't think its hard to find something interesting about math either, and it is immediately applicable, even with what I think is extremely stupid in the form of common core as presented in the USA, you are literally being presented story problems about common every day occurrences and activities.
  - atoav 3y ago
    As someone who routinely teaches (Non-STEM) university students practical applications of math I can assure you that none of the students that told me "I am bad at maths" went out of my class without an understanding of the topics we talked about. Yet I routinely hear a: "Wow, if they told it to me this way during school I might have cared!" or "It really made my head smoke, but it felt good." Step 1 is believing that every person that doesn't have cognitive problems can understand an abstract concept if it is explained well and they got the motivation to understand it. Then you need to create a situation which motivates them to understand it and now you only need to explain it well. Many math teachers fail already at step 1. They believe 90% of their students are too stupid to understand things, while this is just a convinient explaination for their own failures. I once was convinced of being that student. I met one kid that I couldn't teach anything because he would forget things I told him 15 minutes befoee. He was a refugee from Afghanistan and severely traumatized. The truth is that we should look to the best when teaching and we would be stupid if we didn't. And the best are people like 3blue1brown. If your class falls significantly below such a level of clarity and engagement it will suck. During my own math education I had teachers that left out the most fundamental applications. E.g. something like an integral has clear applications, it is a new super power with which you can solve new problems — yet all we did was learning a receipe and solving abstract problems. The fact that it was a super power was something I had to figure out myself, later. And this was common. I even was lucky because I had a good physics teacher who managed to being up a lot of what we learned in math and give it a more practical feel, but most of my friends from other schools were not so lucky.
    - bedobi 3y ago
      This is exactly how my education went. Oh you're not engaged with my shitty teaching and forcing you to do endless abstract nonsensical formulae with zero contextualization or application? Then you're the problem - you have cognitive defects, you are plain dumb and stupid, you are disinterested, you don't care about your education etc etc so I cannot help you. Now let me spend my time on "teaching" the kids who mostly already know what I'm "teaching".
      - latency-guy2 3y ago
        > This is exactly how my education went. No it didn't. I am very confident it did not. All students that make it past grade school go through nearly the exact same sequence and motivating examples beginning from geometry, high school algebra, and then some introduction to calculus if not calculus outright. And the motivating example has always been how to calculate area, and if advanced enough, volume, for all kinds of shapes, regular or otherwise. This is not a recent development, its been the motivating example and the entire purpose for calculus having been invented. I am so confident in this that I am here to call you a terrible student and that, yes, you likely were a terrible student, especially since your characterization is the exact standard excuse I hear from terrible students. So now I have to drill - what was "nonsensical"? What had "zero context"? You immediately have lost the claim of "zero application", so we don't have to go there. If your claim is beyond K-12 math and into university, then I would be too upset to even argue with you if that is your actual position. Making these claims after more than a decade of learning math tells me you have trained yourself to forget all you learned.
        atoav 3y ago
        Interesting form of confidence. I didn't write the comment you replied to, but I wrote the original comment. The first fact I want to have written down is that there are bad math teachers. And sadly it is not uncommon for them to be bad, as I mentioned most of my collegues from other classes and schools had bad math teachers and some of them were people that liked math. Now as an educator I am aware that students are quick to blame other people or the system for their own deficiencies, but I can tell you for a fact that our math teacher failed to explain us what an integral was actually for in an parsable way, even after multiple times of asking. She just knew how to do the formula stuff, she never used it herself on real applications. And when she did explain things, she always did it once, much too briefly in the beginning, so that by the point at which we started doing her always decidedly abstract examples nobody knew what the fuck this was for. As I said, our physics and mechanica teachers were better math teachers than her. As for the integral I had to go and look it up myself, the internet was still young and there weren't many grown ups who knew how to look such a thing up and when I saw the explainations I wondered why nobody ever told us..? I understand btw. why it can be an advantage to understand math in purely abstract ways, but in her case she just didn't want to talk much and stick to the examples. And that is bad teaching. Ah and before we get into a discussion about specifics, like many on this site I grew up and live happily outside of the US, so educational plans etc. might differ.
pylua 3y ago
That is a consistent problem with the education system no matter what the topic is with few exceptions.
- mycologos 3y ago
  I think the economic returns to "decent understanding of X plus decent communication skills" are much higher when X is math than when X is art or language or history, so you need a greater passion for teaching to select it in spite of that fact, and this shrinks the pool of good math teachers relative to other subjects.
- bobajeff 3y ago
  I'm pretty sure math is the most poorly taught subject out of all of them. Social studies, current events, history, literature arts are mostly skills most people use everyday. Math is important so every school is required to teach it however not many schools can. The issue with math is there are never going to be very many good math teachers as that would require many more people who know math. How many adults even know math beyond basic arithmetic?
  - melagonster 3y ago
    Even the basic content from textbook is not real mathematics. the daily work of mathematician is very different to calculate some interesting things.
melondonkey 3y ago
Hard to meet everyone where they are and at the same time give them a relevant practical application for their own life. Good learners just soak it up and look for the application later. But that also doesn’t fit all. It’s hard to even write a pop song that everyone likes so math education that appeals to all is almost impossible
skhunted 3y ago
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.
- atoav 3y ago
  Haven't thought is for decades, but was my environments favourite math tutor, because I managed to ground everything in people's reality and rell them a compelling fiction in which knowing how to do the thing was actually a super-power. You know like the survival tricks certain preppers learn and never use — that, but with math. Even if the examples were sometimes over the top, involved flaming moats and other xkcd-like freakiness I got students where their teachers told me it is hopeless sitting there participating with glowing eyes. Meanwhile in my own math education I had a teacher who made us do integrals for what felt like a year without telling us once what the hell it is needed for. I had to figure that out on my own. My colleagues who didn't care just learned it by hard and forgot it immediately after. But I guess they got thought all the material and got ok grades so their education was a success. What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep.
  - skhunted 3y ago
    What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep. This is precisely what I was referring to about people who come back at a later time and relearn the stuff. They want applications. At the time a class is taken very few actually want to dive into applications. The subject has been taught the way it is taught for a reason.
bawolff 3y ago
> How did folks come up with and it, prove it works and start using it I mean, anything at the university level should include proofs on why it works. I would go as far as to say you aren't really doing math if there are no proofs.
- lupire 3y ago
  elementary level too! Humans crave understanding. This is what we finally have with modern materials like Eureka.
golol 3y ago
Did you not have a physics class around the same time you learned calculus and linear algebra? That makes it obvious what the application is.
constantcrying 3y ago
This is completely asinine. What you say applies to every subject in school. I interpreted poetry, learned ancient history and dead language. Yet somehow the single most useful tool of thought humans have developed needs to justify itself so that you will learn it?
eternityforest 3y ago
I did a (not fully third party reviewed for errors, watch out) project to record all the math related "cool shit I'm glad to have discovered": https://github.com/EternityForest/AnyoneCanDoIt/blob/master/MathELI5.md https://github.com/EternityForest/AnyoneCanDoIt/blob/master/...
jrm4 3y ago
It's really this. I was a "good" student so I got pretty far in college math; and none of it has stuck with me without a real life application. At ALL. What's kind of killing me now, as my kids go through algebra et al, is that now we have a VERY OBVIOUS way to make this interesting and we're severely underutilizing it, which is video games. "Draw a rainbow in Minecraft" or "Figure out the trajectory of that frag grenade" seems just gobsmackingly obvious as a path here.

mycologos 3y ago

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.)

saithound 3y ago
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!).
- abdullahkhalids 3y ago
  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.

Brian_K_White 3y ago

I always liked Lockhart's Lament https://maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf 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 3y ago
Paul Lockhart was my high school teacher! He completely changed my mind about math.

daxfohl 3y ago

The same should be said for engineering design docs tbh

serf 3y ago
absolutely disagree. an engineering design document is about information retrieval, not education. It's not made to entertain or educate about new concepts, it's made to be terse and rigidly structured for the sake of aiding the work of the reader and to provide reliable information recall methods for those reading it. I don't want to know what 'problems are worth attacking' when reading a design document, I want to know what tolerance criteria the hole on the left flange needs to meet. There is more wiggle-room for artistic expression when we're talking about analytical papers like feasibility and failure analysis. It doesn't belong in the design phase. It creates confusion and ambiguity for the reader often, and those two things need not be introduced into design more than they already exist.
- Jensson 3y ago
  > It's not made to entertain or educate about new concepts, it's made to be terse and rigidly structured for the sake of aiding the work of the reader and to provide reliable information recall methods for those reading it. That goes for math papers as well. Both needs to be understood by juniors, both are used by experts for lookup and work.
- eternityforest 3y ago
  I might want to know why the hole on the left flange needs such insane tolerance though. Maybe it's not relevant in a specific version, or maybe I have an idea for how to solve the issue so it can be made cheaper, etc. Maybe it's absolutely integral to the whole application and I should stop wasting my time trying to make a printed PLA version, etc.
constantcrying 3y ago
Absolutely not. Engineering design docs should be terse and to the point. Documentation is not a medium where you want to tell a story, because that makes it instantly much less usable, since people will read it at random parts to attain specific information.

twelfthnight 3y ago

> 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.

johncarlosbaez 3y ago
Everything is always subliminally affecting you. It might as well do it in a helpful way.
- twelfthnight 3y ago
  > everything is always subliminally affecting you Right, but certain methods are more effective than others. This paper is arguing and encouraging exactly how to manipulate more effectively. > It might as well do it in a helpful way Being more effective in teaching I agree is a good thing. But a math paper isn't for teaching, it's for showing a proof or making an argument. I just think we ought to set standards on academic research to remain as neutral as possible to let ideas flourish on merit rather than cunning tricks. EDIT: I get that a career in academia requires all these games to get more citations. Looks at ML research, I feel like abstracts are written by used car salesman nowadays. So like, if you have to do it do it. But we ought to call it out from time to time.
  - elbear 3y ago
    I think it was the word "subliminal" that made you think of manipulation. On the other hand, I read the quote you posted as meeting the reader at their level and guiding them to a clearer, deeper understanding by providing information in a logical, intuitive way. This would mean, for example, providing real-world context for each abstract concept introduced, rather than just leaving the concept by itself together with an abstract definition.
ajkjk 3y ago
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.

dieselgate 3y ago

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.

layman51 3y ago

This really reminds me of a writing course I took called “Writing Stories for Science”. That’s where I first encountered the idea of story beats. The class seemed more focused on the natural sciences and story structures, so I got the impression this must be very difficult to apply to pure mathematical writing. Maybe it’s easier in applied mathematics where there’s a clearer reason that could be explained to a layperson.

hazbot 3y ago
I don't think the point here is to make a math paper understandable to a lay person, but rather make it interesting and contextualize it for other academics.
- 082349872349872 3y ago
  Other academics are already interested and either already have or know where to get the context; that's why the style is the way it is.

js8 3y ago

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 code), so that we could run the state machine on a computer and get a result. However, once you know what it takes to invert boolean functions, you don't need the solution step, you can just quantize your equation (problem) directly to a SAT instance, and let the inversion algorithm do all the hard work. No (elegant and readable) math is required anymore. So I think we better treat mathematics as a "useless" human artifact (like art or chess) rather than something of practical value.

yau8edq12i 3y ago
> 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 be able to give you a proof on demand on statement number 123456789 in some Gödel numbering of statements. What it won't be able to tell you is that the theorem should be called the "intermediate value theorem" and what it means. Math isn't just coming up with formally correct proofs for pre-existing statements. I also don't see what "P vs NP" has to do with anything. > 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 code), so that we could run the state machine on a computer and get a result. I'm a mathematician. What you wrote is just bonkers. Some parts of math are about writing algorithms to solve equations. The vast majority of math isn't.
- js8 3y ago
  My point is, the need for semantics is a human construct, it's not required to solve practical problems. Practical value of MVT is that we can apply it in the process of describing a solution, i.e. an algorithm. But if you have a SAT algorithm that can somehow inherently apply a finite instance of MVT, you no longer need to know what MVT is. And this is at the heart of P vs NP question, how to solve SAT, and once we understand that, all the math that is about solving equations (i.e. that of practical value) will become very boring. Kinda like when a game becomes solved with a computer. (This reminds me of Chomsky and Norvig debate on the machine learning and nature of understanding. I wouldn't think I would take Norvig's position, yet here we are.) Addendum: I am also not arguing that computers writing proofs are a necessity for this, but rather efficiently (as possible) solving SAT instances. You don't need to state a hypothesis (and thus prove it) for an infinite number of cases to solve practical problems. I am also not judging value of math - yeah, it is fun. All I am saying it inherently has a human dimension in the sense we don't need it (assuming we have an efficient SAT solver) to solve practical problems.

culebron21 3y ago

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.

golol 3y ago
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.
- culebron21 3y ago
  That's what I tried to avoid in the first place :)
  - KeplerBoy 3y ago
    But that's the entry point. Well written textbooks, which discuss the right problem are invaluable. If you head straight to google scholar, you're going to have a bad time.
  - constantcrying 3y ago
    So you tried to avoid an instructive text which is set up to allow readers to learn about the details of the subject starting from the ground up? And you are complaining that you can't find a resource which does exactly that?
    - culebron21 3y ago

gumby 3y ago

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.

082349872349872 3y ago
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?
somenameforme 3y ago
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. [1] - https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf
- Someone 3y ago

mayd 3y ago

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 places to publish nontechnical academic writing.

sweezyjeezy 3y ago
> Space in academic journals is too precious to waste on inessential content Not the biggest issue in maths - the arxiv version usually won't match the journal version 1:1
- melagonster 3y ago
  and they publish on internet, solid copy is not popular today.
jcla1 3y ago
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?
Ekaros 3y ago
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.
lupire 3y ago
#5 being exclusionary to people with different/better ideas/practices is not an pillar worth preserving.
Ar-Curunir 3y ago
"Space in academic journals is precious" Well thank god we have preprint servers which have no such stupid requirements.

Tutitk 3y ago

The "dull" version is two times smaller and much easier to read. Hard pass for me. Over time it will probably grow into long-long editorial pieces. I will propably have to use AI to strip down the story mode.

seanhunter 3y ago

This is one of those things that is extremely insidious because it holds a kernel of truth but the author takes it to a place that in my opinion is really unhelpful. For example, his opening paragraph "One of the main problems..." seems fine to me for setting the context, but I would immediately want him to follow with "Let ..." and state the proper definition. All of the extra fluffiness means I have to do two translations - from the fluffy part to the actual maths and then back again - each time to understand what he is getting at. In my opinion, great maths writing is both rigourous and engaging. I would use "Calculus" by Michael Spivak as an example. It's really lovely to read but also concise and elegant and the beauty of (and love for) the maths comes through on every page. The author isn't trying to turn it into a short story and it's not padded out with additional rhetorical bullshit like "And now we come to a key player: the group of deck transformations." That sentence makes me want to puke just a little bit. But all of the above is a matter of opinion. This, for me is a hard nope: 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. I really really hate it when people do shit like this. State things properly even if you need to say something like "don't worry about x y z condition I put there for now which will be explained later". He says you must warn the reader you're doing this but basically I think this is just a hard pass from then onwards. Like if you want to give a simpler version of something, you can by all means do: This is known as seanhunter's theorem, which is usually stated as, if blah blah blah... When x is a real number greater than zero this can be simplified as follows: If x is the number of minutes spent in a meeting and p is the number of participants, then the expected value of the meeting is given by v= r/sqrt(x^3p^2) r~N(mu, sigma^2) ... or whatever. So you give the real version and then the "special case" version that is actually useful most of the time. Like when people give you Fermat's little theorem[1] and they say a^p is congruent with a mod p but that is equivalent to saying if p does not divide a then a^(p-1) congruent with 1 (which is the one you're going to actually use most of the time). [1] https://en.wikipedia.org/wiki/Fermat's_little_theorem https://en.wikipedia.org/wiki/Fermat's_little_theorem

assimpleaspossi 3y ago

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.

hcks 3y ago

No, not everything should be written in the style of a NYT best-seller non-fiction, actually

the_panopticon 3y ago

always a good read on mathematical writing https://www.mathematik.uni-marburg.de/~agricola/material/halmos.pdf https://www.mathematik.uni-marburg.de/~agricola/material/hal...

zogrodea 3y ago

Some ight appreciate the following short paper, relatedly. A quote is extracted below. https://uhra.herts.ac.uk/bitstream/handle/2299/5831/903260.pdf 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."

Retr0id 3y ago

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.

A_D_E_P_T 3y ago

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.

kouru225 3y ago
Putting it on my list
gthrow12345 3y ago
My college advisor gifted me a copy when I graduated, and I passed it along to one of the best students that I had. Great book.
edanm 3y ago
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?

lapinot 3y ago

> 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.

twelfthnight 3y ago
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.

bluenose69 3y ago

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.

datascienced 3y ago
If academic papers were published in HTML with living links on the web it would help. Hypertext solves this but are they not allowed to use modern (1990s+) technology?
- lupire 3y ago
  URLs die. A good citation can be interpreted by technology to search and locate the referenced object.
  - datascienced 3y ago
    As the meme says: why not have both, or even an extension to HTML for a permanent reference that your browser can then resolve using the least defunkt current resolver.

queuebert 3y ago

This comment below the article from the author cracked me up: "Part of why this paper took so long to write is that the file was called boring.tex."

seba_dos1 3y ago

The entirety of math is "human", there's no way for it to neglect that "dimension". (the article's title is "Why Mathematics is Boring")

chrismorgan 3y ago

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. https://www.gutenberg.org/files/4064/4064-h/4064-h.htm#link2H_4_0020 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: 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.

thpl2k3j4324234 3y ago

[flagged]

Ar-Curunir 3y ago
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.

j2kun 3y ago

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.

Ar-Curunir 3y ago
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.

gbacon 3y ago

Thank you. This is beautiful. 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/2016/07/How-to-write-a-great-research-paper.pdf https://www.microsoft.com/en-us/research/uploads/prod/2016/0... https://www.microsoft.com/en-us/research/uploads/prod/2016/07/How-to-give-a-great-research-talk.pdf https://www.microsoft.com/en-us/research/uploads/prod/2016/0... https://simon.peytonjones.org/assets/pdfs/writing-a-proposal-mar23.pdf https://simon.peytonjones.org/assets/pdfs/writing-a-proposal...

lupire 3y ago
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.

woopwoop 3y ago

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.

igorbark 3y ago
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
- samatman 3y ago
  Like everything in mathematics, "obvious" is a term of art. Broadly speaking, it refers to a fact, proof, consequence, which is necessary for the proof to advance, but which is already established elsewhere, so it does not in itself aid in understanding the proof being presented. A proof is either providing a new result, or is proving an established result in a new way. Almost always, a proof will need other results, in a way that isn't "interesting" (another term of art). The point of introducing these results as "obvious" is basically to say "here is something which isn't proven by the proof I'm presenting, we need it, but there's no need to derive it to follow this proof", ideally, with a footnote. As language, it is a bit sly: if something is obvious in the normal sense, it will be left out. It's a problem that the modern style is to elide anything obvious in this sense, rather than in the sense of "anyone who might reasonably read this paper may be expected to know this". But labeling these things as obvious isn't meant in the sense "if you don't know this, you're stupid or uninformed", or in fact "this will be instantly clear as soon as I mention it", it's meant to mean "if you were to follow the breadcrumbs and check up on the 'obvious' thing, it wouldn't help you much in following my proof, so take my word for it. Or, y'know, knock yourself out if this step is interesting to you".

Warwolt 3y ago

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.

jimmar 3y ago

This was the "good" example: > 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.

tombert 3y ago

I don't know what's objectively "correct", but my favorite CS papers are the ones that try and be more entertaining to read. Stuff like "Cheney on the MTA", or the "Lambda the Ultimate" papers are fun to read, while still dumping a lot of interesting information. I also think Lamports papers tend to be more fun simply because they use more tangible analogies for things rather than sticking with formalized mathematics. I kind of view the overly dry, super-formal math/CS papers to be almost a form of gatekeeping. There's a lot of really useful information in a lot of papers, but people don't read them because they rely on a lot of formalisms and notation that are pretty dry to learn about. Sure, I know what a "comonad" and "endofunctor" is, and using terms like that can be useful, but I also think that it can sometimes be better to take a simpler, more grounded approach to things, or at least work with metaphors.

ivanjermakov 3y ago

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.

Ar-Curunir 3y ago
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.

shadowgovt 3y ago

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.

amai 3y ago

It is a long and old tradition in math to explain your findings as obscure as possible to make sure that your competitors cannot follow you. "He is like the fox, who effaces his tracks in the sand with his tail" (Abel about Gauss) https://hsm.stackexchange.com/questions/3610/what-is-the-original-source-for-abels-quote-about-gausshe-is-like-the-fox-wh https://hsm.stackexchange.com/questions/3610/what-is-the-ori...

nso95 3y ago

It seems unreasonable to expect someone to both be an expert in mathematics as well be some great story teller