> I have good friends in US, UK and Russia who have been
> through such competitive mills and have clearly not been
> harmed by them.
I didn't find it to be harmful at all. It did likely steer
me away from a career in mathematics, mainly because I learned
for the first time in my life that I wasn't the best at math.
I studied with and competed against people my age who could
"run circles around me" math-wise. This could have been very
rough on me if my self-image was "great math whiz" -- but
that's not me. Instead, it was liberating in a way, because
I no longer felt "obligated" to a career in mathematics.
And it definitely pushed me to improve my reasoning and
thinking skills, but that was certainly a good thing.
> Even so, it seems to me that these contests
> give the wrong idea about what good math
> (and much else) truly requires.
> Arete (the pursuit of excellence) is not the same
> as javelin throwing...
Well, the skills I learned and developed in training for
those Olympiads were quite relevant to good math. In
order to score well on an Olympiad, one needs to have
aptitude for mathematics, a broad and comprehensive
understanding across a wide range of the field, and the
ability to express one's ideas and methods succinctly
On the other hand, the Olympiad is a closed-book exam;
if real mathematicians didn't have reference libraries
and the desire and ability to use them well, the progress
of mathematics would be severely impaired. Similarly,
the Olympiad is an individual examination; real world
mathematicians (well, *respected* real world mathematicians)
have to collaborate with their peers on a regular basis --
besides joint papers, they have formal and informal peer review.
Lastly, an Olympiad competitor begins an Olympiad problem
with the knowledge that a solution exists which should take
him no more than about two hours to discover, formulate,
perfect, and "publish" -- real world mathematicians rarely
have that luxury. :-)