I was reading a note of Hojoo Lee on inequality which is written for International Math Olympiad (IMO) participants. Although he writes that “target readers are challenging high schools students and undergraduate students“, it appears to be quite advanced.
It occurred to me to ask, do these IMO problems contribute towards research work in math? Do these math notes/books give good overview for research work?
I am not interested in examples of Fields Medal winners who had previously participated in the IMO.
Answer
There are very different areas of mathematics, some are more theory-oriented, some are more problem-oriented. Theory-oriented areas (like e.g. algebraic geometry) are built from bottom to top, while problem-oriented areas (like combinatorics, discrete optimization) offer you a bunch of methods that are suitable for solving problems and you need to cleverly combine them. The spirit of the latter areas is much nearer to the "Maths olympiad feeling" while the former areas require different skills.
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