- #36

mathwonk

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This makes me reflect briefly however on the enjoyment aspect, as I happen to enjoy thinking about geometry or topology, more than about some aspects of analysis, which to me are very hard.

I tried and failed to get a PhD in several complex variables because I was always somewhat in pain while thinking abut the topic. It was too complicated and too hard to mentally envision the "infinities" required for analysis.

On the other hand I eventually managed to envision geometric objects having 12 or 15 complex dimensions, and even add something to their history. Then my exposure to several complex variables came in handy in algebraic geometry of higher dimensions.

Topology, which I liked, seemed almost too "easy' (you can always deform things so wildly to get whatever you want), so I landed somewhere in the middle, in algebraic geometry. It had enough geometry to be visualizable, but enough analysis to be somewhat unintuitive. So I wanted a subject that was hard enough to challenge me, but not so hard and unintuitive that I could not imagine how to proceed.

Ironically it now seems to me that the most powerful tools in algebraic geometry are borrowed or adapted from algebraic topology and several compelx variables, (cohomology, sheaves, charcateristic classes), and now quantum physics!

Fortunately after years and years of study, and the opportunity to teach courses in calculus and a few in analysis, and better to talk to brillaint friends in these subjects, I am beginning to enjoy that too.

I never liked combinatorics either, so what is the hottest area of examples in algebraic geometry for the last decade? "toric" varieties, with a combinatorial flavor.

We seem to enjoy what we understand, and not what we do not. So if you want your listeners to enjoy your talks or your courses, try to help them understand.

And eventually everything you ever learned or had a chance to elarn, may pop up as useful in your own specialty, so don't sdespise or neglect anything when its time comes around.

I took GH Hardy as something of a model as a young man, but that is hazardous. I liked his toast: "to pure mathematics; may she never be useful to anyone!"

this isolationist attitude is not healthy for a young person, as it can shut him off from the sources of inspiration available in physics and applied math. perhaps hardy only meant he opposed military destruction using science, but I took it as an excuse not to become well rounded.