I’m sorry if this question goes against the meta for posting questions – I attached all the “beware, this is a soft-question” tags I could.
This is a question I’ve been asking myself now for some time. In most areas, there’s a “cut off age” to be good at something. For example, you’re not going to make the NHL if you start playing hockey at 20. It just won’t happen.
So my question then, how late is too late to start studying math and make a career out of it? By “start studying math” I mean, to really try to understand and comprehend the material (as opposed to just being able to do well in a formal, intuitional environment).
I don’t mean this from a “do what you love, its not too late” motivational perspective. I mean this from a purely biological perspective; at approximately what age has your brain’s capacity to learn effectively and be influenced by your learning stop? When does the biological clock for learning new math run out?
My reasoning for asking this question is (for those who care): I love math. Really I do. But , having spent the first 21 years of my life in sports/video games/obtaining a degree in a scientific field which I care nothing of/etc, despite all my best attempts at trying to learn math, am I just too late starting to ever actually be good enough at it to make it a career? I’ve almost completed my second degree (in Math), but find that in many cases, despite how I look at a problem, I lack the intuition to comprehend it. I’m going to single him out (sorry), only as an example, but Qiaochu Yuan is my age.
Note 1: If this question isn’t a suitable post, I won’t be offended at all if you vote to close – I know this question borders what’s acceptable to ask.
Note 2: Thanks to everyone for reading and taking the time for the great responses. Really appreciate it!
Karl Weierstrass was in his 40’s when he got his PHD. There are a dozen other counterexamples, a number fairly recent. A good set of examples can be found in the thread on MO here.This myth of “science is a game for the young” is one of the falsest and most destructive canards in modern society. Don’t listen to it. You only get one life and when it’s over, that’s it. When you’re dead a hundred million years, you’ll be dead the tiniest most infinitesimal fraction of all the time you’ll ever be dead. So stop listening to career advice from teenagers, grab a calculus book and get to work. That’s my advice.