AoPS article "Pros and Cons of Math Competitions":

- http://www.artofproblemsolving.com/Resources/AoPS_R_A_Contests.php

Quite often mathematicians argue that math olympiads do not correspond to their actual research work which seems to be true. And thus, it is implied, an IMO medal does not mean anything.
Research work seems to deal with open-ended problems where it is unsure whether a solution can be found at all and if so what effort it takes. In math olympiad it appears that a solution exists and can be found in a limited scale of time given sufficient innate capability, motivation, passion and good training.

Apparently Mr. Nobel did not like math too much and we have the following comparable prizes being awarded every four years http://www.mathematik-olympiaden.de/IMOs/fields.html :

- Fields Medal http://mathworld.wolfram.com/FieldsMedal.html
- Nevanlinna Prize: http://mathworld.wolfram.com/NevanlinnaPrize.html

Among the 8 winners of 1998 and 2002 events we find four IMO medal winners, one of them won the national olympiad of the Soviet Union but was prevented for non-math reasons to participate in the IMO, one of them won the USA undergraduate competition Putnam and one of them is coming from a country that did not participate in the IMO back then.

I have not checked more in detail for 2006 but I think it is widely known that Grigori won a perfect score at IMO 1982 and Terence participated several times at IMO (IMO 1986-1988) at a very young age (and seems to be the youngest IMO medal winner). He in collaboration with Ben Green (IMO 1995/1996) showed that a sequence of prime numbers contains arbitrarily long arithmetic progressions. Yuri Matiashevich (gold medal IMO 1964) solved Hilbert's Tenth Problem.

Of course in terms of admission different universities put varying emphasis on math olympiads. Some argue in favour of diverse student body, well-roundedness or put more focus on different ways to identify mathematical talent via research projects as Intel Science Talent Search Siemens Westinghouse Competition, research with a professor at the local university etc.

But of course not everybody goes on to solve an extremely important math problem and possible receive some prize for it. What happens to the more regular mathletes? There is an interesting study by Alexander Karp about those people in Saint Petersburg (Leningrad), Russia, Soviet Union:

- Thirty Years After: The Lives of Former Winners of Mathematical Olympiads (also appended)
-- http://pocketknowledge.tc.columbia.edu/home.php/viewfile/download/5706
- School 239 is so famous. It even got an article on wikipedia:
-- http://en.wikipedia.org/wiki/Saint_Petersburg_Lyceum_239

I recently did a little bit of research and tried to look up all of my classmates from MOP 1988 (which was the only year I went to MOP and the middle of rrusczyk's 3 years at MOP). It's been 20 years(!), so I couldn't track down a couple of people and sadly one of our classmates has passed away, but for the rest of us, there was an almost exact 1/3-1/3-1/3 split into three categories:

- math professors
- professors in a subject other than math (physics and CS mostly if I remember correctly, but one person is an economics professor)
- working outside of academia, either for the government (guess where?) or in the private sector (including, of course, me and rrusczyk at AoPS)

How many people participated in MO(S)P back then? What were other positions in the private sector except for AoPS? Do you think your observations will change over time a lot?

Advice on mathematics competitions by Terry Tao.

Here are some interesting discussions about math education in America.