In contrast, all of the science and engineering disciplines can make use of very interesting math. Not deep compared to research math, but used in a much more interesting way than in finance. E.g when you study the statistics of markets, you are just playing a game, and don't care that much about external reality per se. On the other hand if you study the statistics of DNA or gene expression, you are doing real science.
I think the best advice to a young person studying math is what was given to me at the age when I was doing the IMO (and interestingly, after I graduated by someone else): Don't neglect statistics.