Having come to mathematics late in my life, I don't have the youthful, competitive spirit of a high school math whiz. Yet in plodding through my introduction to calculus, and edging nervously away from the Rigorous Approach, I know that I am in some sort of competition anyway. I am not competing with anyone else, but with myself, and even more fundamentally, with the subject. I am currently doing review problems before moving on to the next chapter, or, perhaps, inning.

I was never the competitive sort, especially when I was young. Not only is it, as the evolutionary psychologists and neuro-scientists assert, a characteristic of my gender not to want to compete, but I was never raised that way either. Winning and losing were reserved only for tennis, where there was no real meaning to the wins or losses among friends, and for our Boston Red Sox, who were experts at losing. The worlds of math and science, though, are from the beginning as competitive as organized sports. It is related to the gender issue which I cannot speak of lest I be accused of wrong thinking and those dreadful "sweeping generalizations."

The great English mathematician G.H.Hardy, in his autobiographical and mathematical memoir, "A Mathematician's Apology," expresses this in a famous paragraph:

"…I thought of mathematics in terms of examinations and scholarships; I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively."

Hardy was also a "court tennis" and squash player, and wild about cricket, which only reinforces the image of mathematician as athlete, or perhaps athlete as mathematician. For a young mathematician or physicist nowadays, not only are there examinations and scholarships, but science fairs and math tournaments and finally, the Math Olympiad which tests high school students in the USA, which then leads to the International Mathematical Olympiad, where the best youths (and a few maidens) from all over the world compete. I looked at the problem sets that these fortunate few tackled, and it would take me ages to solve just one of them, let alone a whole test full of them. Math is a competitive sport.

And then of course after ace-ing the examinations, winning the scholarships, and scoring in the Olympiad or the science fair, there is the ever-more-brutal competition of undergraduate and graduate schools, which winnows out all but the (pun) Hardiest of people. There in the classrooms and the laboratories and the conferences, competition goes on at all levels. After the PhD, the post-doc. After the post-doc, if he keeps "winning," the academic or industrial job. And after years of competing in research, publishing, politicking, jockeying for position, the favored few reach the high point: academic tenure. But that is only the lower reaches of the science and math competition, for in the lofty heights above live the superstars: Nobel Prize winners, or in the case of mathematics, Fields Medal winners. It is amazing to contemplate the recent case of Grigory Perelman, who, against all sense of competition, refused this most-coveted prize in mathematics, even though he earned it.

But my approach to my extremely modest math effort is rather like my participation in tennis, where I could hit a ball off the backboard, bouncing it back to myself, for hours on end. I didn't do much actual playing. My experience of any kind of competitive play was very limited. There's plenty of competition in the art world, but as with math or science, I have avoided it. I don't know whether that's a good or a bad thing.

There is a lot going on in my life currently, with day job, art, and learning new graphics programs taking up much of my time. Some days, I only get to do a few math problems. I have been wondering whether I should contrive some sort of artificial pressure to make me do more math work and progress faster. There is no Olympiad for me to win. There is nothing about my math and science work that matters to anyone but myself, and there are no coaches who encourage me to stay in training, or even ask about my progress. There is no career ahead of me no matter how much I learn. And yet every time I approach those math problems, I tackle each one with some anxiety, since the review problem will test me to see whether I have really learned anything. If I get it wrong, I'm disappointed, as if I've hit the tennis ball into the net. But if I get it right, I feel as though (to change the game to one I have never played) I've sunk the ball into the basket.

Posted at 3:08 am | link