This is my answer to the same question posed on the Academia Stack Exchange. It is therefore licenced under CC-BY-SA 3.0.

Question

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?

Answer

I think of Olympiad problems more as “parlour tricks”. They’re really difficult, and it’s super-impressive if someone’s good at them, but the skills are very different to the skills you need in research. As a big example of a difference: the Olympiad rewards quick accurate leaps of reasoning, because you’re under such time pressure. Research rewards long-term grit and persistence through blind alleys and repeated failure.