Comment by tkgally
15 hours ago
I studied math hard for several years in college and graduate school—purely out of interest and enjoyment, not for any practical purpose. That was more than forty years ago, but Bessis's description of the role of intuition in learning and doing math matches my recollection of my subjective experience of it.
Whether that youthful immersion in math in fact benefitted me in later life and whether that kind of thinking is actually desirable for everyone as he seems to suggest—I don't know. But it is a thought-provoking interview.
I also studied it and got several degrees, but I don't think that it actually benefited me. I think high school math is incredibly important to be able to think clearly in a quantitative way, and one university-level statistics course, but all the other university math... I dont think it helped me at all. I am disappointed by it because I feel that I was misled to believe that it would be useful and helpful.
Have you ever ascribed numbers to real life personal problems? I find that managing to frame something bothersome into a converging limit somehow, really dissolves stress.. A few times at least.
That’s an interesting approach. I don’t think I’ve done that myself, but I can see how it could be helpful.
One positive effect of having studied pure mathematics when young might have been that I became comfortable with thinking in multiple layers of abstraction. In topology and analysis, for example, you have points, then you have sets of points, then you have properties of those sets of points (openness, compactness, discreteness, etc.), then you have functions defining the relations among those sets of points and their properties, then you have sets of functions and the properties of those sets, etc.
I never used mathematical abstraction hierarchies directly in my later life, but having thought in those terms when young might have helped me get my head around multilayered issues in other fields, like the humanities and social sciences.
But a possible negative effect of spending too much time thinking about mathematics when young was overexposure to issues with a limited set of truth values. In mainstream mathematics, if my understanding is correct, every well-formed statement is either true or false (or undecided or undecidable). Spending too much time focusing on true/false dichotomies in my youth might have made it harder for me to get used to the fuzziness of other human endeavors later. I think I eventually did, though.
Thanks for sharing. The reverse direction here, I'm trying to go from fuzziness to the exactness of those true/false dichotomies, haha. The way I've been attacking mathematics, it's like a tree in the forest, one could start with the axioms and from the base reach each branch and the leaves and fruits. But I've just been walking around the tree, looking at the leaves and fruits and branches from different directions to see ways of climbing without doing a whole lot of climbing. What I mean is I've been thinking and reading in an imprecise way a whole lot without actually juggling symbols with pen and paper, haha. Or a roadtrip analogy, I've done little driving and a lot of map ogling. At least I won't miss the turns when I pick up some speed.