I read several articles saying that most mathematicians have the peak of their career before 30 and after that they don't do much significant work. Although this is a simplification of the reality, the truth is that in math many people do major breakthroughs before 30, a lot more than in other fields of science. I was wondering what is the cause of it? On one hand I would expect that with age you get more experience and you have more directions in which you can go when trying to solve a problem so more chances to succeed. On the other hand mathematics is older than any other science, so one would expect that you need a much longer time to reach the modern knowledge, compared to other sciences, before doing any breakthrough. So why is the reality so different from the expectations?