I think that pretty much everyone who knows any number of mathematicians and has talked to them at any length about their work has received exactly this sort of counterbalancing. As someone in a similar position to Scott, I’ve heard it more times than I can count, and I’ve honestly come to resent it somewhat. I’ve been told no end of times about how the beauty and elegance of “real” math, and how unrepresentative the sort of calculating work done at lower levels is of that sort of mathematics, but this is pretty much always being expressed by people who didn’t have certain difficulties with the work at lower levels that the people they’re expressing it to did.
I’ve been on the other end of this a lot, trying to teach stuff to people which seems to me to be so intuitively, even beautifully obvious once you look at it from the right perspective, that it seems impossible for a person of any intellectual capacity not to grasp it, only to find that it takes a herculean effort on both our parts for them to make any sense of it at all. It’s forced me to accept that there’s a lot more human variability than I once thought in the capacity to be really bad at things.
Like Scott, there are some kinds of “real math” which I have a reasonable amount of familiarity with and fluency in. And I have a fair amount of curiosity about and enthusiasm for mathematical curiosities of a certain sort. But I’ve never been able to muster the slightest bit of enthusiasm for doing math except to the extent that it lets me work out non-math things I’m interested in the answers to. I would love to like math more for its own sake, because there are times when figuring things out which I’m interested in the answers to requires learning more math which is a lot easier if I can appreciate it for its own sake throughout the steps I have to make it through. But lacking that immediate motive, I find much of the necessary learning incredibly dull and frustrating.
I think that pretty much everyone who knows any number of mathematicians and has talked to them at any length about their work has received exactly this sort of counterbalancing. As someone in a similar position to Scott, I’ve heard it more times than I can count, and I’ve honestly come to resent it somewhat. I’ve been told no end of times about how the beauty and elegance of “real” math, and how unrepresentative the sort of calculating work done at lower levels is of that sort of mathematics, but this is pretty much always being expressed by people who didn’t have certain difficulties with the work at lower levels that the people they’re expressing it to did.
I’ve been on the other end of this a lot, trying to teach stuff to people which seems to me to be so intuitively, even beautifully obvious once you look at it from the right perspective, that it seems impossible for a person of any intellectual capacity not to grasp it, only to find that it takes a herculean effort on both our parts for them to make any sense of it at all. It’s forced me to accept that there’s a lot more human variability than I once thought in the capacity to be really bad at things.
Like Scott, there are some kinds of “real math” which I have a reasonable amount of familiarity with and fluency in. And I have a fair amount of curiosity about and enthusiasm for mathematical curiosities of a certain sort. But I’ve never been able to muster the slightest bit of enthusiasm for doing math except to the extent that it lets me work out non-math things I’m interested in the answers to. I would love to like math more for its own sake, because there are times when figuring things out which I’m interested in the answers to requires learning more math which is a lot easier if I can appreciate it for its own sake throughout the steps I have to make it through. But lacking that immediate motive, I find much of the necessary learning incredibly dull and frustrating.