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.
Math writing is dull when it neglects the human dimension
131–140 of 186 posts
Re: Math writing is dull when it neglects the human dimension
#132I always liked Lockhart's Lament 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.
Paul Lockhart was my high school teacher! He completely changed my mind about math.
Re: Math writing is dull when it neglects the human dimension
#133As 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…
While gatekeeping is definitely a thing, I really suspect it's not the major incentive here. In writing (both prose and code!) there is always a question of target audience, which inevitably excludes the not-target audience. Personally, for a field in which I'm an expert, it's really annoying to continually wade through introductory material and hand-holding just to get to some small nugget of substance. In that case…
> Honestly, with software development, I find it disappointing that our social conventions currently conflate "readability" with "comfort and familiarity to Generic Programmer" instead of something more useful like "facilitates domain understanding and insight to the primary developers".
It's sort of a similar effect: most software is written by software people for other software people, just like most math is written by math people for other math people.
I personally have had the experience more than once of a mathematician apologizing for their code style but then handing me code that I find to be more straightforward and readable than usual.
What specific conventions do you think would facilitate domain understanding and insight?
Re: Math writing is dull when it neglects the human dimension
#134This 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.
Re: Math writing is dull when it neglects the human dimension
#135I’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 th…
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.
Re: Math writing is dull when it neglects the human dimension
#136Some possible counterarguments: 1. Mathematics is a lot more abstract than it used to be. 2. Mathematics is a lot more specialised than it used to be. 3. Non-mathematical content is inaccessible to those who don't read English. 4. Space in academic journals is too precious to waste on inessential content. 5. The style is part of a universal mathematical culture so you should fit in. 6. There are many alternative plac…
#5 being exclusionary to people with different/better ideas/practices is not an pillar worth preserving.
Re: Math writing is dull when it neglects the human dimension
#137Earlier quoted context omitted.
I mean.. It's no different than a story being written better instead of worse. The dry paper is just worse in every way, at both the author's goals and your goals.
> This may require “watering down” the results being described — stating corollaries or special cases instead of the full theorems in their maximal generality. Sometimes you may even need to leave out technical conditions required for the results to really be true. This is a trade off, don't you think? Without the marketing, the paper would be more complete and correct.
No, your exercpt is not complete and correct.
"So, the introduction to a math paper should set the scene as simply as possible"
The introduction is not the whole paper.
Re: Math writing is dull when it neglects the human dimension
#138Thank 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/2016/0... https://www.microsoft.com/en-us/research/uploads/prod/2016/0... https://simon.peytonjones.org/assets/pdfs/writing-a-proposal...
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.
Re: Math writing is dull when it neglects the human dimension
#139I 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…
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?
URLs die. A good citation can be interpreted by technology to search and locate the referenced object.
Re: Math writing is dull when it neglects the human dimension
#140I’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 th…
> 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.
elementary level too! Humans crave understanding.
This is what we finally have with modern materials like Eureka.