Hi! I'm a high school student who’s deeply passionate about math. I’m definitely not a genius, but I aspire to become a mathematician someday as it’s honestly the only thing that keeps me awake at night, besides my girlfriend.
I’ve read a lot of posts saying that you don’t need to win the IMO or be an olympiad star to become a great mathematician, and I completely believe that. But there’s something I still don’t fully understand.
People often say olympiad math and research math are very different. But research mathematics is also about solving extremely hard problems that nobody has solved before, which sounds similar, at least superficially, to olympiad problems. So what exactly is the difference in mindset, creativity, or skill between olympiad math and actual mathematical research?