Does the International Math Olympiad help research mathematics?
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.