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9I don't know the Putnam exam, but Math Olympiads already require you to write in formal and well constructed ways. I speak from experience only on a national level (in Germany), but it was always necessary to formulate correct proofs and I can hardly imagine it would be different at the IMO.– dirkkCommented Mar 14, 2017 at 11:39
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7"I think that there is only a weak correlation between capable researchers and Math Olympiad champions." Over which population? Do you mean that an IMO participant isn't much more likely to become a good mathematician than a random guy on the street.– JiKCommented Mar 14, 2017 at 12:48
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12Successful Math Olympiad competitors are no more "math savants" than trained researchers: their success is the result of a long, thorough, and deep training process. The whole "special math genius" trope is harmful both to society at large (where it puts people off of mathematics) and within mathematics (where it fools us into valuing apparent genius over hard work).– Greg MartinCommented Mar 14, 2017 at 19:54
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4The correlation between IMO success and research success is indeed less than complete, but by calling it "weak" you are understating it a lot. Everyone from the German IMO team in my years (2004-2006) is involved in research (maths or CS) today. Same holds for the majority of the top 20 from IMO 2004 (just one example). This is not to say that the rest have failed at research -- they might have chosen a career that suits them better.– darij grinbergCommented Mar 15, 2017 at 3:53
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4At every International Congress of Mathematicians since 1990, at least one of the Fields Medalists was previously a medalist at the IMO. Seven of them got perfect scores. (Fewer than 200 people have received a perfect score through 1995, the most recent year relevant to the Fields Medal.)– A. RexCommented Mar 15, 2017 at 6:27
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