[mark-t]

Math education is so bad right now that any genetic differences are drowned out almost entirely. Of all the mathematicians I've met (including IMO gold medalists, Fields medalists, etc.), there seems to be little correlation with siblings, at least beyond what you would expect from having parents who emphasize learning math.

To answer your question, if you want to contribute significantly, you will need to study hard for several years, but it is possible. One of the best mathematicians I know well didn't have any interest until he was 16, and he's now 25 or so.

[narag]

"...there seems to be little correlation with siblings, at least beyond what you would expect from having parents who emphasize learning math."

I'd bet for a set of negative factors. For you to be 100%, you need to have full 15% of genes (maybe there are a lot involved, so it could be very improbable to have more than 10% of that 15%), 30% of early nurture and 40% of favorable social conditions (good environment, or just not being poor that lets out a big part of humanity) and the rest of luck, effort and good teachers.

The lack of any of these conditions could explain why the siblings are not so bright. The lack of genetic conditions and the early nurture could also ruin more easily the posibilities.

"Genetic" is also broad. It could be quicker thinking, focus, even a illness that forces a child to stay home reading instead of playing outdoors.

[maximilian]

Wow, 16 is sooo old. I'm sure plenty of great mathematicians didn't know what they wanted at 16 either.

25 is pretty young still I think. Thats only 3 years into a PhD, so really I wouldn't expect anyone (except super geniuses) to make many achievements by that age. I'd say 30 between 27 and 30 seems like a pretty solid age, as you've reached a peak with your PhD and you're still young and inquisitive and hopefully humble.

[mark-t]

Ask around. 16 is quite late to start taking math seriously and end up at the very top. He wasn't doing math for fun. He wasn't asking himself mathematical questions. He wasn't doing math competitions. He had no knowledge outside of what was taught in school to students at his grade level. This is freakishly uncommon, but he shows it's possible.

25 is young. He is just a few years into his PhD, and he hasn't made many major achievements (he's been a grader for the IMO, written one paper that's still being refereed for publication). The point is that he's noticeably better than I am at almost every branch of mathematics except combinatorics, and he had no interest until he was 16.