Two types of mathematician
So, I was an undergrad mathematician, and planned to become an academic, but bailed out of my PhD and became a programmer instead. I made notes as I was reading the various articles.
My strong suit in maths was analysis. I just never 'got' algebra at all and didn't touch it after the first year.
Weirdly I was very good at linear algebra/matrices/spectral theory/fourier analysis. But all that seemed like a geometrical, intuitive theory about high-dimensional spaces to me. I had very strong reliable intuition there, but I never had any intuition, or idea about how one might go about acquiring one, for rings/fields/groups or mathematical logic.
I never liked any sort of symbol-manipulation. I felt I understood things if and only if I could make mental pictures of what was going on that would imply the answers 'as if by magic'.
M. Meray's endeavours seem unappealing. I appreciate them in the abstract but cannot imagine getting interested. Prof. Klein's conducting sphere seems a fascinating masterstroke.
Feynman/Einstein are definitely 'what I'd be if I was twenty times better'. I recognise their ways of thinking, at least as they explained them.
I agree wholeheartedly with Arnold's rant.
I'm ambivalent on the problem-solver/theorizer distinction. I think I'm more of a theorizer, but problem-solving is important and they both matter. I'd have been proud to have contributed in either way.
Maths is very visual for me. The symbols mean nothing without the pictures.
As a programmer, I:
love lisp, and found it mind blowing when I first found it. By default I use a lisp variant called Clojure both personally and professionally, although I've tried almost everything. I avoid java and c++ if I can.
have occasionally tried Haskell, and feel that I ought to understand it, but it feels like programming with one hand tied behind my back. An awful lot of extra effort for no gain.
am quite fond of python, although I use it as a watered-down lisp and avoid all its OO facilities.
adored "Why Arc isn't especially Object Oriented"
have never tried template metaprogramming, C++ is just too dirty for me, although I love C itself.
like both vi and emacs, and was originally a vi user, but these days I use emacs almost exclusively, and have done ever since I discovered what a joy it is as a lisp editor.
I think that all, with the exception of emacs, puts me strongly on the analysis/intuition side of things and weakly confirms the suggested dichotomy and its relationship to programming styles.
But it's been a long time since I ate corn-on-the-cob. When I try to visualise it I see myself eating it in rows rather than spirals. But I don't want to go out and find some, because then I'd bias the result. Somehow I have to catch myself in the act of eating it unconsciously. Any suggestions?