Too old to start math

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.

21 is not old at all. I personally know heaps of people my age (32) who started out at 18 as salesclarks/BA or BCom majors/lawyers/bookeepers etc and ended up having a PhD degree in some advanced math areas and landed a job in academia or industry.

My personal case: I got a lousy BCom degree with little math at 22 and then worked in a primitive banking job. After a few years I realized I was growing stupid, so decided to do what I secretly always liked but never really had the balls to do: math and stats.

So I moved to another country, did a Masters degree in Computational Statistics, (2nd level honours) then started on PhD in Computer Science (mathematical modeling of AI). After 6.5 years of math I'm, like $n^n$ times smarter than I was at 22, I got a postdoc job in my area and got awarded a Doctoral degree this morning.

In Israel kids are expected to serve in the army when they are 18, and they serve for three years (men do, women serve two years). After this period it is common to find yourself questioning what you should do with yourself and not many people have answers. Therefore it is common to take another two years to work and travel the world before settling down and starting your academic education.

This means that most students in Israel begin their undergrad studies around the age of 23-24.

That been said there are considerably less mathematics students, and many of them start sooner. I started at 22, but I studied both with kids that didn't serve in the army and were 19-20 and people who took longer to settle for math and were 25.

So if you are just 21 and you want to start with mathematics, you're still younger than the average Israeli freshman.