8 ms·

I see. What I'm talking about is mathematics for the sake of mathematics. Any training aimed at mathematicians needs to emphasize rigor. Otherwise, there will

by wayn3 10y ago

I see. What I'm talking about is mathematics for the sake of mathematics. Any training aimed at mathematicians needs to emphasize rigor. Otherwise, there will be a bunch of impotent mathematicians. Not what we want. I'm not opposed to teaching engineers "just the calculations". But such classes should be organised by their departments, not the mathematicians'. Your guys know better what you need to know. This has nothing to do with elitism, though. A mathematician needs to know how mathematics works. Most other disciplines do not. I wouldn't claim that engineers are only allowed to earn their degrees if they pass math classes, thats just how colleges organise their course requirements.

kxyvr 10y ago
As a counter point, I've a PhD in applied mathematics and I believe there's plenty of elitism in the field. Unless you're a logician following a very specific set of reduction rules that can be verified mechanically, a proof is largely just an argument that something is true or not. Just because something is true doesn't mean the argument for it is strong, nor comprehensible. Part of the elitism within the field is that, at times, the community places pride on being as incomprehensible as possible because we should be smart enough to fill in the "trivial" details. That's morally wrong and it turns people away from the field. Further, it locks out a huge number of people who are not specialists from accessing the material. Awhile back, I had a coauthor on a paper screaming at me in his office that it was condescending for me to include a full set of calculations for a proof that I authored. We had the room the paper for the result. I, as the author of the proof, couldn't follow the proof without the full set of calculations. We actually walked around the office and most people agreed with my coauthor. Although I ultimately prevailed and kept the calculations, it's an example of the underlying problem. Namely, yes, a large portion of the field is elitist. "I don't need these calculations to understand the result, so why should my readers?" Math is not so cut and dried that there is precisely the minimum number of statements to describe a problem or give a proof. I very, very strongly believe in rigor. We can be rigorous and not be a dick in how we write or present material.
- demonshalo 10y ago
  Thank you! I am 100% certain that had authors of a lot of papers that I have read included some examples and perhaps even calculation results, I would have understood and perhaps even been able to reason about some of their publications a whole lot better than I currently can. Just the mere inclusion of a few examples makes a world of difference. The idea that X is clear to everyone and therefor we do not need to exemplify it for the reader is really back-breaking. Especially when you are not coming form a background that includes years of expertise within said domain!
  - umanwizard 10y ago
    Sure, but math papers are not written for general audience; they're written for mathematicians. Elucidation that would be useful for the general public is very difficult or impossible to write in such a way that it wouldn't be extraneous distracting fluff for mathematicians. It would also make most papers dozens of times longer. I'm not exaggerating here: I think you could probably state and prove the results from basic one-variable calculus (assuming as axioms some basic properties of the field of real numbers) in 10-20 pages in such a way that mathematicians would understand it, whereas beginner calculus textbooks are regularly over 1000 pages long. A hypothetical research mathematician who didn't know calculus would find the 20-page version way easier to understand than a slog through Stewart's 1300-page book. What you want is undergraduate-level textbooks, not research papers. Good textbooks do contain all the stuff you want: examples, calculations, motivation, etc. I can recommend some if you are interested in a particular field.
    - kxyvr 10y ago
      Some of the point that I was trying to make is that a large number of papers are incomprehensible for people in the field as well and often not for any good reason. Yes, sometimes it's hard to come up with good illustrations or examples, but, frankly, they help everyone. Let me give an example of a good way to do this. To me, Mark Embree is a really good mathematician. He also works in a somewhat esoteric area called pseudospectra, which helps us understand non-normal operators and, ultimately, how to effectively solve differential equations. Look at the following page: http://www.math.vt.edu/people/embree/EF.html http://www.math.vt.edu/people/embree/EF.html Mark isn't dumbing down his material, but he is giving context for why it matters as well as graphical descriptions of how some of these ideas work. This is some of why I admire Mark's work. It's not just the technical results, but working to come up with better ways to relate the material.
dangsucksdick 10y ago
You sound like a cunt

by wayn3 10y ago

kxyvr 10y ago

As a counter point, I've a PhD in applied mathematics and I believe there's plenty of elitism in the field. Unless you're a logician following a very specific set of reduction rules that can be verified mechanically, a proof is largely just an argument that something is true or not. Just because something is true doesn't mean the argument for it is strong, nor comprehensible. Part of the elitism within the field is that, at times, the community places pride on being as incomprehensible as possible because we should be smart enough to fill in the "trivial" details. That's morally wrong and it turns people away from the field. Further, it locks out a huge number of people who are not specialists from accessing the material. Awhile back, I had a coauthor on a paper screaming at me in his office that it was condescending for me to include a full set of calculations for a proof that I authored. We had the room the paper for the result. I, as the author of the proof, couldn't follow the proof without the full set of calculations. We actually walked around the office and most people agreed with my coauthor. Although I ultimately prevailed and kept the calculations, it's an example of the underlying problem. Namely, yes, a large portion of the field is elitist. "I don't need these calculations to understand the result, so why should my readers?" Math is not so cut and dried that there is precisely the minimum number of statements to describe a problem or give a proof. I very, very strongly believe in rigor. We can be rigorous and not be a dick in how we write or present material.

demonshalo 10y ago
Thank you! I am 100% certain that had authors of a lot of papers that I have read included some examples and perhaps even calculation results, I would have understood and perhaps even been able to reason about some of their publications a whole lot better than I currently can. Just the mere inclusion of a few examples makes a world of difference. The idea that X is clear to everyone and therefor we do not need to exemplify it for the reader is really back-breaking. Especially when you are not coming form a background that includes years of expertise within said domain!
- umanwizard 10y ago
  Sure, but math papers are not written for general audience; they're written for mathematicians. Elucidation that would be useful for the general public is very difficult or impossible to write in such a way that it wouldn't be extraneous distracting fluff for mathematicians. It would also make most papers dozens of times longer. I'm not exaggerating here: I think you could probably state and prove the results from basic one-variable calculus (assuming as axioms some basic properties of the field of real numbers) in 10-20 pages in such a way that mathematicians would understand it, whereas beginner calculus textbooks are regularly over 1000 pages long. A hypothetical research mathematician who didn't know calculus would find the 20-page version way easier to understand than a slog through Stewart's 1300-page book. What you want is undergraduate-level textbooks, not research papers. Good textbooks do contain all the stuff you want: examples, calculations, motivation, etc. I can recommend some if you are interested in a particular field.
  - kxyvr 10y ago
    Some of the point that I was trying to make is that a large number of papers are incomprehensible for people in the field as well and often not for any good reason. Yes, sometimes it's hard to come up with good illustrations or examples, but, frankly, they help everyone. Let me give an example of a good way to do this. To me, Mark Embree is a really good mathematician. He also works in a somewhat esoteric area called pseudospectra, which helps us understand non-normal operators and, ultimately, how to effectively solve differential equations. Look at the following page: http://www.math.vt.edu/people/embree/EF.html http://www.math.vt.edu/people/embree/EF.html Mark isn't dumbing down his material, but he is giving context for why it matters as well as graphical descriptions of how some of these ideas work. This is some of why I admire Mark's work. It's not just the technical results, but working to come up with better ways to relate the material.

dangsucksdick 10y ago

You sound like a cunt