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Your comment runs counter to my experience learning math and the experience of basically every person I know with graduate or higher education in the subject. S

Your comment runs counter to my experience learning math and the experience of basically every person I know with graduate or higher education in the subject. Sure you might be trying to learn something you're not ready for if you're frustrated, but even then I don't think anything past 300 level math will be realistically frustration-free the first time you're exposed to it. It feels to me like you're splitting hairs with your comment here: learning or doing new math is fundamentally a frustrating process, even for mathematicians. If you're doing math and it's not frustrating, you have an exceptional grasp of it and it's not new to you, which usually develops after persevering through many frustrating exercises. Technically speaking every mathematical proof is a proof "from first principles" - but if I teach you analysis and linear algebra, you're not going to just derive vector and tensor analysis easily, no matter what first principles you're working from. Beyond the first few years of undergrad math everything is so far removed from first principles that it's virtually certain you will struggle with some of the material unless you have significant prior exposure to it. There isn't really a way around that. You have the exposure or you don't, but math you haven't learned never just "falls into place", so to speak, even if it's relatively easier for some than others. In fact, every former math graduate student I can think of has told me the first year or so felt like wallowing in confusion. Likewise "working at the edges until it feels easy" seems like a distinction without a difference, in my opinion (but reminds me of Grothendieck). I don't see a meaningful difference between the frustration of software engineering and the frustration of math, either. If you're not doing research mathematics, day to day applied math work becomes just as much about routine, "grab your toolkit and put things together" work as programming.

dmos62 8y ago
I'll make an observation that you seem to equate incomplete comprehension and frustration, exploration and struggle, confusion and discomfort. An intellectual challenge can degrade to something unpleasant, like any experience, but it most definitely isn't inherently that.
- throwawaymath 8y ago
  I guess what I'm saying is the original comment's opening statement is vacuous. We can argue semantics over whether or not it's "unpleasant" or "frustrating" to learn difficult new abstractions in math, but the more important point is that 1) learning math is difficult for approximately everyone, even accomplished mathematicians, and 2) it's silly to avoid taking advice from people who had a difficult time learning math, because that rules out almost all your potential teachers. Even as an enjoyable experience it's frequently confounding. If it weren't, Wiles' famous analogy about stumbling around in a dark mansion looking for lights wouldn't be as oft-repeated as it is. If you don't want to use the word "frustration", then fine don't use it, but I think that misses the substance of the article author's point. You could adequately replace the statement in question with, "Be willing to endure ungodly amounts of confusion."
  - romwell 8y ago
    Well, not knowing where you are is not the same as feeling confused, in the same way as a wanderer who doesn't know where they are isn't necessary lost. What I hear you saying can be seen as a gym analogy: no pain, no gain. The hidden part here is that gym rats actually enjoy the experience, whatever words you use to describe it, and for many others who are after the results it's merely painful. If you are in grad school: in my opinion, graduate schools are supremely successful in sucking all the joy out of doing mathematics (and life). The whole system needs to be scrapped. I agree that one should not avoid taking advice on math from someone who struggled with it - because, as you note, that's all of us. However, I would not take advice on a subject from someone who's never really enjoyed doing it.

dmos62 8y ago

I'll make an observation that you seem to equate incomplete comprehension and frustration, exploration and struggle, confusion and discomfort. An intellectual challenge can degrade to something unpleasant, like any experience, but it most definitely isn't inherently that.

throwawaymath 8y ago
I guess what I'm saying is the original comment's opening statement is vacuous. We can argue semantics over whether or not it's "unpleasant" or "frustrating" to learn difficult new abstractions in math, but the more important point is that 1) learning math is difficult for approximately everyone, even accomplished mathematicians, and 2) it's silly to avoid taking advice from people who had a difficult time learning math, because that rules out almost all your potential teachers. Even as an enjoyable experience it's frequently confounding. If it weren't, Wiles' famous analogy about stumbling around in a dark mansion looking for lights wouldn't be as oft-repeated as it is. If you don't want to use the word "frustration", then fine don't use it, but I think that misses the substance of the article author's point. You could adequately replace the statement in question with, "Be willing to endure ungodly amounts of confusion."
- romwell 8y ago
  Well, not knowing where you are is not the same as feeling confused, in the same way as a wanderer who doesn't know where they are isn't necessary lost. What I hear you saying can be seen as a gym analogy: no pain, no gain. The hidden part here is that gym rats actually enjoy the experience, whatever words you use to describe it, and for many others who are after the results it's merely painful. If you are in grad school: in my opinion, graduate schools are supremely successful in sucking all the joy out of doing mathematics (and life). The whole system needs to be scrapped. I agree that one should not avoid taking advice on math from someone who struggled with it - because, as you note, that's all of us. However, I would not take advice on a subject from someone who's never really enjoyed doing it.