This kinda blew up after I left so let me elaborate.
When I say some fields you need formal education in a controlled setting, there's a few examples I can give to provide context.
If you want to go into medicine, you can't borrow a friend and just try things on them. By the time you go into the field any mistake you make becomes critical and it's difficult to log hours and gain experience without a formal educational environment.
To practice law you need to be able to pass the bar, you need to understand decades of case history, legal precedent and how the entire system functions so that you can feasibly operate within that system.
To get into management you can potentially gain experience in volunteer organizations but to do so you're likely going to have enough of a go-getter attitude to be elevated to those positions in the first place. It's not quite the same as saying "I'm going to read these books and learn management."
To go into various fields of engineering there are a number of systems to be understood, sometimes expensive equipment involved and literal danger to other people if things aren't done properly. You can certainly tinker your way into an interest, but you need the formal education in a controlled environment.
There are many other fields that fit within that bubble.
For most of computer science you can pick up and book, sit in front of your laptop and work, learn, experiment, try, fail, learn, improve continuously for virtually no cost other than your own time. You need a goal, then to work towards that goal you learn what you need to accomplish it and pick up those pieces to begin. When it sucks, you learn why and figure out how to improve it. You start optimizing. You need to make something faster you learn how it works under the hood. You need to hook up to some other system you learn about apis. You need to make the interface better, you learn about UX.
The cost to learn is time and that's why this field is constant learning.
I agree with other posters that most people are pursuing advanced math in their spare time. Neither am I but I don't often need to invoke advanced math. I know there are areas where one would need it more, but these days I do not know many people in this field who do.
The crux of my point is simply that, some of the best programmers I know have never gone to college and are 100% self taught. There are very few other fields that you can say that about.
That's all I was getting at.