I am a maths enthusiast and have been exposed to maths olympiad problems for some time. I wanted to know how does a math Olympian do in undergraduate courses of mathematics, statistics or computer science. Are the problems given on the courses even harder than maths Olympiad? And do the maths olympians score full marks in their semester exam? Thank you.
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4$\begingroup$ Somewhat relevant: Why are the contents of contest maths so different from contents of degree-level maths? AND Learn university maths or train for high school competitions: which is better? AND Are high-school contest problems "harder" than college mathematics? AND Is high school contest math useful after high school? (continued) $\endgroup$– Dave L RenfroCommented Nov 14, 2023 at 8:49
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3$\begingroup$ AND Advantages of Mathematics competition/olympiad students in Mathematical Research AND any other questions linked to any of these questions (see upper right-side of web page for each of these questions). $\endgroup$– Dave L RenfroCommented Nov 14, 2023 at 8:52
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$\begingroup$ I would expect top olympiad participants or Putnam fellows also to do exceptionally well if they choose undergraduate math ... But sometimes they choose other fields (computer science, medicine, law...) (example: Feynman chose physics) and also do exceptionally well. Were there any olympiad champs who flunked out of math? Probably, but we don't hear of them. $\endgroup$– Gerald EdgarCommented Nov 15, 2023 at 15:46
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Mathematics is many things. Solving tricky problems is part of it, but there is also learning theory and new concepts and ways of thinking, and even developing routine.
I would expect a person with good results of mathematics olympiads and similar contests to have a lot of skills that are useful in studying mathematics, like problem-solving skills (including persistence and not giving up in the face of hard problems), good routine and good basic knowledge of certain fields of mathematics.
However, this does not guarantee success in understanding new theories and ways of thinking. These are specific to a given field or subfield.
All other things being equal, I would generally expect nice results, but only if the student does the required work. There is still a lot to learn. Thinking that one is already finished and can coast along leads to failure within a couple of years, and is a definite risk if everything has always been easy and one is "clever".
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$\begingroup$ I don't much about Olympiads aside from one competition I entered in a group once at University, but it was enough to experience that a part of the deal was working well under time pressure. Something you may not experience in any other context (maybe as an engineer, technician/operator like a pilot for instance, or some kind of sports it's relevant, gaming too). What is your goal? Is it just the knowledge, or is the competition a part of it? $\endgroup$ Commented Nov 13, 2023 at 18:54
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7$\begingroup$ @SoumyadipDas The comment hear asks if study math and old problems will make you a good olympiad competitor. Maybe. But maybe you don't have that particular kind of mathematical talent. The question you actually asked was whether doing well on olympiads would translate into doing well in advanced math. Yes, probably - but many (perhaps most( mathematicians are good at math and not particularly good at olympiad like problems. $\endgroup$ Commented Nov 13, 2023 at 20:38
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$\begingroup$ @SoumyadipDas That sounds like a different question; if it is not answered yet in the linked questions, you could ask it as a new one. $\endgroup$– TommiCommented Nov 15, 2023 at 14:42
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$\begingroup$ Success in problem competitions involves a number of factors, some of which are relevant for future work in mathematics (knowledge, cleverness)but some of which are not related to mathematics (getting a good night's sleep, getting lucky). I took the Putnam exam twice and did far better the second time than the first. I believe most of the difference was luck --- I happened to have a good day the second time. $\endgroup$ Commented Nov 16, 2023 at 19:35