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You and the author are conflating two different things. The pure math community probably DOES feel that popularizing only applied mathematics is betraying pure

You and the author are conflating two different things. The pure math community probably DOES feel that popularizing only applied mathematics is betraying pure mathematics, and they're probably right. We don't really teach proofs outside of highschool geometric proofs and maybe a single class in university. However there's no good reason why we can't popularize both applied AND pure mathematics.

thanatropism 9y ago
There's this joke in applied math departments that the best way to spook a pure mathematician is to whisper in his ear "We've found an use for your theorem..."
- nonbel 9y ago
  "We've found an use for your theorem..." I'd think that would be more likely to spook the English department.
  - dredmorbius 9y ago
    Rhetoric.
    - dredmorbius 9y ago
      So ... this is a thing. https://en.m.wikipedia.org/wiki/Rhetoric https://en.m.wikipedia.org/wiki/Rhetoric
- wolfgke 9y ago
  I found an application for a theorem that was originally proved by the authors because for its interesting geometrical meaning. One of the authors who I talked to really liked my application. So in my impression pure mathematician might not be motivated by applications, but if other people find cool applications, they typically love it.
  - smilliken 9y ago
    There's another traditional joke among pure mathematicians: as hard as we resist, every theorem will eventually find its way to practical application. More of an aphorism than a joke, but we'd all laugh.
  - pmiller2 9y ago
    Is there a link to a paper? :)
chrisdbaldwin 9y ago
The real tragedy is that pure mathematics is hidden from students for too long and many opt-out of that path in favor of "Actuarial Science" and applied maths. Real talk: pure maths was way more fun, interesting, and applicable to my life as a software engineer than all the applied math and modelling that I wrote/learned/etc. Pure mathematics expanded my mind unlike any other subject matter.
- extr 9y ago
  I think you're right that pure math is hidden too long, and with too many "applied" detours along the way. When I was getting my BS in math, I started hearing concepts my junior/senior year that would have done a lot to clear up the motivation and context for lower level classes, even if wouldn't understand them fully until later. Particularly in regards to linear algebra. I did go the Actuarial Science/applied math route in the end, so your comment rings true, but I'm not sure I would characterize it as a bad thing. I wasn't going to be a world-class researcher and the marginal return on a graduate degree in pure math wasn't there. That said, there was a small feeling of "And now the time for fun and games is over" when I stopped studying pure math. I enjoy my job, but math provides a certain satisfaction that business problems do not.
- mncharity 9y ago
  > The real tragedy is that pure mathematics is hidden from students Physicists make a similar complaint. "Why would anyone want to study physics, when kids are not shown any interesting physics?" Chemistry education research characterizes pre-college chemistry education content as incoherent, leaving both students and teachers confused and deeply steeped in misconceptions. Biology education... starts by deemphasizing it's core organizational principle, and goes downhill from there. > The real tragedy Here's another. "It has been more than a decade since science education research surprised us with how badly science education was failing students. But even now, how often are students told? Instead, K-13, students have been left to think their confusion and cluelessness, are strictly their own fault, their own failing. Left to think science is boring. They are not told that these are known defects of the wretched content we're giving them. Fixing the content is hard. But telling them isn't. At what point does our failing to notify them become an ethical failure?" > pure maths was way more fun, interesting, and applicable to my life [as a software engineer] It can be fun to create ELI5-ish stories about math in everyday life. Math as recognizing patterns. So for instance, moving one way on a "circular" path, you come back around to the same position. As with boardgames, clocks, parking, etc. Missed doing something at lunch today... perhaps try lunch tomorrow. Missed a parking space and can't back up... perhaps drive around the block. Category theory for kids.
spyhi 9y ago
Speaking of the lack of education in proofs and popularizing math, do you (or anyone else here) know of good resources to practice and learn more about proofs? I've asked several professors and TAs in my CS program and they say "practice," but they couldn't point to any good tools for self-teaching and I don't really feel confident evaluating the material I've found on my own.
- fmoralesc 9y ago
  Velleman's "How to Prove It" is a nice textbook on how to develop mathematical proofs. You can apply the techniques to any other field you are interested in, and that is probably the best way to practice: by trying to prove things you already have some intuitive sense about.
  - spyhi 9y ago
    Picked up a copy, thank you! And thanks for the suggestion on proving things in area I already have an intuition for, maybe I'll do that in conjunction with reading the book.
- deleted 9y ago
  [deleted]
cshenton 9y ago
As someone who ended up majoring in pure mathematics, I always thought it was a shame that theres this wall of arithmetic and calculus between you and the first pure mathematics class. I suck at those, but I do well with abstractions and proofs. Makes me wonder how many pure mathematicians the field misses out on.
- surement 9y ago
  My university kept the pure math courses for "honors" students; I'm still outraged by this to this day. It's very misleading and as someone who didn't do great in the "regular" (i.e. rote repetition/memorization calculus and linear algebra courses), it kept me out until a prof in one of these classes introduced me to real math. At that point it was a much steeper learning curve to switch to the "honors" route but I'm glad I did it.
- thearn4 9y ago
  It does seem strange that you have to typically "pay your dues" with 4-ish semesters of calculus (calc i, ii, ii, diffy-q, and maybe pre-calc) before you take anything else. It's very strange as a gate-keeper to the subject.
jcranberry 9y ago
I got a BA from NYU and took a fair amount of grad classes and spent most of my time in CIMS. Firstly I'd probably want to hear what you think of as applied mathematics, because if you're talking about the field of applied mathematics that lies outside of engineering and physics, it gets about as much "popularization" as pure mathematics. Putting that aside, of the professors who had pure focuses, I'd say more often than not they tried to do their responsibilities as educators and put forth examples to try and make the material more accessible—but that kind of thing seemed to be how they thought on the matter. Actually, the applied mathematicians were very similar. I felt that most of their thoughts were constructive and there wasn't really any sense of comparison with the traitorous physicists or anything. In the first place, before any popularization of mathematics can occur, it needs to be introduced in a way that doesn't leave all our secondary school students traumatized for their entire education, which goes back to the education system.
mrkgnao 9y ago
> popularizing only applied mathematics is betraying pure mathematics I'd say it's betraying mathematics.
gpawl 9y ago
We can't popularize pure mathematics because, by its definition, pure mathematics is not related even tenuously to every day life, so popularization requires that the audience do years of idiosyncratic study.

thanatropism 9y ago

There's this joke in applied math departments that the best way to spook a pure mathematician is to whisper in his ear "We've found an use for your theorem..."

nonbel 9y ago
"We've found an use for your theorem..." I'd think that would be more likely to spook the English department.
- dredmorbius 9y ago
  Rhetoric.
  - dredmorbius 9y ago
    So ... this is a thing. https://en.m.wikipedia.org/wiki/Rhetoric https://en.m.wikipedia.org/wiki/Rhetoric
wolfgke 9y ago
I found an application for a theorem that was originally proved by the authors because for its interesting geometrical meaning. One of the authors who I talked to really liked my application. So in my impression pure mathematician might not be motivated by applications, but if other people find cool applications, they typically love it.
- smilliken 9y ago
  There's another traditional joke among pure mathematicians: as hard as we resist, every theorem will eventually find its way to practical application. More of an aphorism than a joke, but we'd all laugh.
- pmiller2 9y ago
  Is there a link to a paper? :)

chrisdbaldwin 9y ago

The real tragedy is that pure mathematics is hidden from students for too long and many opt-out of that path in favor of "Actuarial Science" and applied maths. Real talk: pure maths was way more fun, interesting, and applicable to my life as a software engineer than all the applied math and modelling that I wrote/learned/etc. Pure mathematics expanded my mind unlike any other subject matter.

extr 9y ago
I think you're right that pure math is hidden too long, and with too many "applied" detours along the way. When I was getting my BS in math, I started hearing concepts my junior/senior year that would have done a lot to clear up the motivation and context for lower level classes, even if wouldn't understand them fully until later. Particularly in regards to linear algebra. I did go the Actuarial Science/applied math route in the end, so your comment rings true, but I'm not sure I would characterize it as a bad thing. I wasn't going to be a world-class researcher and the marginal return on a graduate degree in pure math wasn't there. That said, there was a small feeling of "And now the time for fun and games is over" when I stopped studying pure math. I enjoy my job, but math provides a certain satisfaction that business problems do not.
mncharity 9y ago
> The real tragedy is that pure mathematics is hidden from students Physicists make a similar complaint. "Why would anyone want to study physics, when kids are not shown any interesting physics?" Chemistry education research characterizes pre-college chemistry education content as incoherent, leaving both students and teachers confused and deeply steeped in misconceptions. Biology education... starts by deemphasizing it's core organizational principle, and goes downhill from there. > The real tragedy Here's another. "It has been more than a decade since science education research surprised us with how badly science education was failing students. But even now, how often are students told? Instead, K-13, students have been left to think their confusion and cluelessness, are strictly their own fault, their own failing. Left to think science is boring. They are not told that these are known defects of the wretched content we're giving them. Fixing the content is hard. But telling them isn't. At what point does our failing to notify them become an ethical failure?" > pure maths was way more fun, interesting, and applicable to my life [as a software engineer] It can be fun to create ELI5-ish stories about math in everyday life. Math as recognizing patterns. So for instance, moving one way on a "circular" path, you come back around to the same position. As with boardgames, clocks, parking, etc. Missed doing something at lunch today... perhaps try lunch tomorrow. Missed a parking space and can't back up... perhaps drive around the block. Category theory for kids.

spyhi 9y ago

Speaking of the lack of education in proofs and popularizing math, do you (or anyone else here) know of good resources to practice and learn more about proofs? I've asked several professors and TAs in my CS program and they say "practice," but they couldn't point to any good tools for self-teaching and I don't really feel confident evaluating the material I've found on my own.

fmoralesc 9y ago
Velleman's "How to Prove It" is a nice textbook on how to develop mathematical proofs. You can apply the techniques to any other field you are interested in, and that is probably the best way to practice: by trying to prove things you already have some intuitive sense about.
- spyhi 9y ago
  Picked up a copy, thank you! And thanks for the suggestion on proving things in area I already have an intuition for, maybe I'll do that in conjunction with reading the book.
deleted 9y ago
[deleted]

cshenton 9y ago

As someone who ended up majoring in pure mathematics, I always thought it was a shame that theres this wall of arithmetic and calculus between you and the first pure mathematics class. I suck at those, but I do well with abstractions and proofs. Makes me wonder how many pure mathematicians the field misses out on.

surement 9y ago
My university kept the pure math courses for "honors" students; I'm still outraged by this to this day. It's very misleading and as someone who didn't do great in the "regular" (i.e. rote repetition/memorization calculus and linear algebra courses), it kept me out until a prof in one of these classes introduced me to real math. At that point it was a much steeper learning curve to switch to the "honors" route but I'm glad I did it.
thearn4 9y ago
It does seem strange that you have to typically "pay your dues" with 4-ish semesters of calculus (calc i, ii, ii, diffy-q, and maybe pre-calc) before you take anything else. It's very strange as a gate-keeper to the subject.

jcranberry 9y ago

I got a BA from NYU and took a fair amount of grad classes and spent most of my time in CIMS. Firstly I'd probably want to hear what you think of as applied mathematics, because if you're talking about the field of applied mathematics that lies outside of engineering and physics, it gets about as much "popularization" as pure mathematics. Putting that aside, of the professors who had pure focuses, I'd say more often than not they tried to do their responsibilities as educators and put forth examples to try and make the material more accessible—but that kind of thing seemed to be how they thought on the matter. Actually, the applied mathematicians were very similar. I felt that most of their thoughts were constructive and there wasn't really any sense of comparison with the traitorous physicists or anything. In the first place, before any popularization of mathematics can occur, it needs to be introduced in a way that doesn't leave all our secondary school students traumatized for their entire education, which goes back to the education system.

mrkgnao 9y ago

> popularizing only applied mathematics is betraying pure mathematics I'd say it's betraying mathematics.

gpawl 9y ago

We can't popularize pure mathematics because, by its definition, pure mathematics is not related even tenuously to every day life, so popularization requires that the audience do years of idiosyncratic study.