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I did some undergraduate research and ended up getting published. My initial drafts were written with prose so that I (and hopefully any novice) could understan

by hgtr 7y ago

I did some undergraduate research and ended up getting published. My initial drafts were written with prose so that I (and hopefully any novice) could understand. However, my professor wasn’t happy with it so I got some help from one of his grad students to re-write it. By the end of it I could barely understand my own paper. IMO the final paper had too much technical jargon which was convoluting some simple concepts. Kinda made me disenchanted with the academic world. Still have to give credit to my prof and the grad student, without their edits it probably wouldn’t have been published.

echelon 7y ago
This is one of the reasons why I pursued engineering instead of a hard science. Mathematics in particular feels like an ivory tower with a bunch of gatekeeping. Better language and grammar around core concepts could improve accessibility, but few in the field that I've encountered seem to care about that. Biology and chemistry are a bit better, but there are still improvements that could be made. You can't easily go from zero to biochem or ochem, and I don't think that has to be the case. Gen chem and gen bio just suck at presenting themes and concepts and instead focus on being a smorgasbord of facts (that you later have to amend or unlearn). Computer science and electrical engineering are a walk in the park by comparison. We have all sorts of interactive tools and visualizations of algorithms and analysis. We keep refining and making the onboarding process easier and more accessible.
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hannob 7y ago
So I find this interesting, because it seems to confirm a suspicion I held. I "only" did some undergrad math during my computer science (but due to a lack of specialization at my university back then it was "real math", i.e. we took the same courses as the math students). My impression often was that a lot of this stuff isn't so hard if you "get to it", but it's clouded in a lot of complicated language that makes it sound harder than it really is. I never dared to postulate that this is a more general problem of math, but your words sound like that's exactly what is happening. Do you think there's a way forward to make math more accessible by using simpler language without sacrificing correctness?
- mathgenius 7y ago
  Absolutely. It's a problem with academia in general. Academics don't get rewarded for explaining things in an easy to understand way. Moreover, it is often a huge amount of work to distill results down like this. And if you succeed the response you may get is "well that is obvious". Anyway, this is my counter argument to the "formalization of mathematics": why don't we incentivize people to bring some clarity to the exposition? If mathematics is suffering from faulty proofs, then I have little sympathy. Make it simpler, organize the concepts. Muscular calculations only go so far.
  - ncmncm 7y ago
    In other fields, writing survey articles is (or was, recently) an appreciated activity. Survey articles are explicitly supposed to bring people up on the important results and current state of a subject.
  - skela224 7y ago
    There's the idea that pure math papers should not have a "Conclusion" section, where the author summarizes what has been done and says a few informal words. This doesn't seem to help the exposition but is nonetheless prevalent: if you haven't paid attention to the proofs and derivation, they aren't going to retell what happened in plain plain language. e.g. look at this advice from the academia stackexchange, to a young aspiring mathematician: "If you're relatively young and inexperienced and hoping for best results on the rapid publication of your work in strong journals, I would stick pretty mercilessly to the format: (i) strong introduction motivating your work and explaining clearly the value added both in the results themselves and the techniques of proof and (ii) the rest of the paper contains careful proofs of all the results, in a very clear, linear, easy to follow fashion, e.g. "Section A.B: Proof of Lemma C".
- I_AM_A_SMURF 7y ago
  > My impression often was that a lot of this stuff isn't so hard if you "get to it", but it's clouded in a lot of complicated language that makes it sound harder than it really is. I never dared to postulate that this is a more general problem of math, but your words sound like that's exactly what is happening. I "only" have a masters degree in Math, but this sounds really wrong to me. Most advanced math concepts are complex and can take months to understand for someone with an unrelated math background (e.g., say, Lebesgue measure theory or Galois theory). I wouldn't even know how to start teaching something like that to someone who doesn't have a formal mathematical background.
simion314 7y ago
Are you sure though that your extra stuff was actually on correct an on point? AFAIK in math you have the primary notions, the axioms then all the previous definitions and proofs, maybe I am imagining somethng different then what actually happened though, an example would be good but it may not be possible for you to remember or express it in a comment here.
Silhouette 7y ago
IMO the final paper had too much technical jargon which was convoluting some simple concepts. This is symptomatic of IMHO the biggest single problem with the world of mathematics today. This discipline should be about developing ideas based on rigorous foundations and logic, which is a useful and important purpose. Once you have understood those ideas, even "advanced" results often seem quite simple and intuitive, and we can take that understanding and apply it to other work if helps us to make useful progress. However, the amount of needlessly obscure terminology, poor notation and just plain bad writing in formal papers make the whole field absurdly inaccessible, even to many who might have no trouble understanding the underlying concepts and important results. Just imagine what would happen if we tried to write engineering specs or software the way postgraduate mathematics research is done. We'd be trying to debug source code where every identifier was a single character, taken from one of three or four different alphabets, with several of them looking similar enough to mistake one for another, with a bunch of combining accent modifiers on top that were used to fundamentally change the semantics of the program, interspersed with comments by someone who needs a remedial class in basic writing skills, full of technical terminology that is defined in terms of other technical terminology from other software packages, except that sometimes the meaning is subtly different in this context but that isn't noted anywhere on the screen at the time, resulting in needing to spend half an hour doing a depth-first-search of all the definitions only to find that a function whose only identifier is the name of the developer who wrote the second version (because the first person to work on it already has another function bearing their name) is actually equivalent to what a programmer would write as const DAYS_IN_WEEK := 7 I write this as someone who studied mathematics to a high level and has touched on the field many times since in connection with heavily mathematical software development. It's the worst sort of closed-world gate-keeping, and we could do so much better, but sadly inertia and vested interests are not our friends in this matter.

by hgtr 7y ago

echelon 7y ago

This is one of the reasons why I pursued engineering instead of a hard science. Mathematics in particular feels like an ivory tower with a bunch of gatekeeping. Better language and grammar around core concepts could improve accessibility, but few in the field that I've encountered seem to care about that. Biology and chemistry are a bit better, but there are still improvements that could be made. You can't easily go from zero to biochem or ochem, and I don't think that has to be the case. Gen chem and gen bio just suck at presenting themes and concepts and instead focus on being a smorgasbord of facts (that you later have to amend or unlearn). Computer science and electrical engineering are a walk in the park by comparison. We have all sorts of interactive tools and visualizations of algorithms and analysis. We keep refining and making the onboarding process easier and more accessible.

deleted 7y ago
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deleted 7y ago
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hannob 7y ago

So I find this interesting, because it seems to confirm a suspicion I held. I "only" did some undergrad math during my computer science (but due to a lack of specialization at my university back then it was "real math", i.e. we took the same courses as the math students). My impression often was that a lot of this stuff isn't so hard if you "get to it", but it's clouded in a lot of complicated language that makes it sound harder than it really is. I never dared to postulate that this is a more general problem of math, but your words sound like that's exactly what is happening. Do you think there's a way forward to make math more accessible by using simpler language without sacrificing correctness?

mathgenius 7y ago
Absolutely. It's a problem with academia in general. Academics don't get rewarded for explaining things in an easy to understand way. Moreover, it is often a huge amount of work to distill results down like this. And if you succeed the response you may get is "well that is obvious". Anyway, this is my counter argument to the "formalization of mathematics": why don't we incentivize people to bring some clarity to the exposition? If mathematics is suffering from faulty proofs, then I have little sympathy. Make it simpler, organize the concepts. Muscular calculations only go so far.
- ncmncm 7y ago
  In other fields, writing survey articles is (or was, recently) an appreciated activity. Survey articles are explicitly supposed to bring people up on the important results and current state of a subject.
- skela224 7y ago
  There's the idea that pure math papers should not have a "Conclusion" section, where the author summarizes what has been done and says a few informal words. This doesn't seem to help the exposition but is nonetheless prevalent: if you haven't paid attention to the proofs and derivation, they aren't going to retell what happened in plain plain language. e.g. look at this advice from the academia stackexchange, to a young aspiring mathematician: "If you're relatively young and inexperienced and hoping for best results on the rapid publication of your work in strong journals, I would stick pretty mercilessly to the format: (i) strong introduction motivating your work and explaining clearly the value added both in the results themselves and the techniques of proof and (ii) the rest of the paper contains careful proofs of all the results, in a very clear, linear, easy to follow fashion, e.g. "Section A.B: Proof of Lemma C".
I_AM_A_SMURF 7y ago
> My impression often was that a lot of this stuff isn't so hard if you "get to it", but it's clouded in a lot of complicated language that makes it sound harder than it really is. I never dared to postulate that this is a more general problem of math, but your words sound like that's exactly what is happening. I "only" have a masters degree in Math, but this sounds really wrong to me. Most advanced math concepts are complex and can take months to understand for someone with an unrelated math background (e.g., say, Lebesgue measure theory or Galois theory). I wouldn't even know how to start teaching something like that to someone who doesn't have a formal mathematical background.

simion314 7y ago

Are you sure though that your extra stuff was actually on correct an on point? AFAIK in math you have the primary notions, the axioms then all the previous definitions and proofs, maybe I am imagining somethng different then what actually happened though, an example would be good but it may not be possible for you to remember or express it in a comment here.

Silhouette 7y ago

IMO the final paper had too much technical jargon which was convoluting some simple concepts. This is symptomatic of IMHO the biggest single problem with the world of mathematics today. This discipline should be about developing ideas based on rigorous foundations and logic, which is a useful and important purpose. Once you have understood those ideas, even "advanced" results often seem quite simple and intuitive, and we can take that understanding and apply it to other work if helps us to make useful progress. However, the amount of needlessly obscure terminology, poor notation and just plain bad writing in formal papers make the whole field absurdly inaccessible, even to many who might have no trouble understanding the underlying concepts and important results. Just imagine what would happen if we tried to write engineering specs or software the way postgraduate mathematics research is done. We'd be trying to debug source code where every identifier was a single character, taken from one of three or four different alphabets, with several of them looking similar enough to mistake one for another, with a bunch of combining accent modifiers on top that were used to fundamentally change the semantics of the program, interspersed with comments by someone who needs a remedial class in basic writing skills, full of technical terminology that is defined in terms of other technical terminology from other software packages, except that sometimes the meaning is subtly different in this context but that isn't noted anywhere on the screen at the time, resulting in needing to spend half an hour doing a depth-first-search of all the definitions only to find that a function whose only identifier is the name of the developer who wrote the second version (because the first person to work on it already has another function bearing their name) is actually equivalent to what a programmer would write as const DAYS_IN_WEEK := 7 I write this as someone who studied mathematics to a high level and has touched on the field many times since in connection with heavily mathematical software development. It's the worst sort of closed-world gate-keeping, and we could do so much better, but sadly inertia and vested interests are not our friends in this matter.