Cathy’s post touched off a lot of discussion of math contests, and whether they do or do not, in her formulation, suck. My thoughts on this are pretty simple.

**Big good thing about math contests:** They reveal that math is more than what’s taught in school, and that there’s a whole community of kids around the world who are passionate about math.

**Big bad thing about math contests:** They help promote the idea that the most important thing about math is whether you’re the best at it.

Of course you can design your contest to provide more of the big good and less of the big bad. The question isn’t so much whether the good minus the bad is positive; it’s whether there are other ways of getting at the good that avoid the bad. I think programs like Hampshire and MathCamp and PROMYS and Ross are like this. But they clearly don’t scale to the size of an AMC. Mary O’Keeffe‘s comments on Cathy’s blog were particularly interesting, since they give a good sense of what math contests are like in 2011 for those of us whose direct experience is substantially less recent.

Some people, I think, don’t think my big bad is so bad. I disagree. Somebody on my Facebook feed recently linked to this letter from algebraist Donald Weidman to *Science*, headed “Emotional Perils of Mathematics.” Weidman numbers among these perils the following frustration:

“The history of mathematics makes plain that all the general outlines and most of the major results have been obtained by a few geniuses who are not the ordinary run of mathematicians. These few big men make the long strides forward, then the lesser lights come scurrying in to fill in the chinks, make generalizations, and find some new applications; meanwhile the giants are making further strides.”

This is so profoundly wrong it makes my teeth hurt. Mathematics is like Earthball. The weight of our ignorance is tremendous and all of us push together to move it a bit to one side over the course of our lifetimes. We may vary in strength but what we have in common is that there’s very little we can do alone.

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