This is a great point, and I think it shows why people don't study math in their spare time. It's the same reason why most people aren't body builders with 5% body fat: it takes a tremendous amount of hard work.

Not only that, but the work isn't glamorous or particularly creative. In my teens, I always though I was "bad" at math -- I never did the homework, didn't do the supplementary exercises, had an "intuitive" understanding that wouldn't translate when exam time rolled around, and I consistently got C's and F's.

In college, I decided to take things more seriously and I remember in Calc I-III doing literally every single problem in the books. If I missed any problem, I would do it over and over again until I got it right. "Miraculously," I started getting A's in math classes.

Sadly Calc iii is not “real” math, just an applied version of what newton created 300 years ago. Real math starts at analysis and abstract algebra. It is extremely inefficient to learn this kind of math completely by yourself since there is a specific ‘math intuition’ that is hard to gain without a great teacher.

That seems a little harsh as a reply to the previous comment - calc 3 is math, but sure, upper division or graduate math also requires the ability to prove things, which is why people who did will in calc-3 might not necessarily do well in more advanced courses until they learn the additional skills. But it's not like the ability to apply theorems and calculate accurately is orthogonal to the ability to do proofs - the attention to detail and ability to keep track of the steps is certainly similar, I would argue.

You dont need to be a graduate in math to prove things. Check out the IMO and tell me it isn't real math, and it's only highschool level.

I'd guess Khan Academy was among the first to provide such teaching. Is it "self-taught", I don't know (I think it qualifies, though). It can be done.

Reading the article, the issue doesn't seem to be that math is particularly hard compared to other STEM fields.

Rather, to be productive in maths, you need a really high level. Before your PhD, chances is that you can't do something meaningful in the field. It means that your degree is the only proof of your level.

So the idea is : you can teach yourself maths but in the order to become a working mathematician, you need to do it all the way up until the end, with little help besides books.

Contrast with programming, after a few weeks, you will be able to write working software, maybe get an internship or even a low level job. You can then work your way up. You don't have to be at the top just to start working or make meaningful contributions.

Even a monkey can write a simple program, that's easy. However, to come up with something unique in computer science field, can easily take decades of study and research.

Math is the purest form of art humans can produce.I'd say one can learn a fair bit of it on his own and be relatively knowledgeable,but..There are many many things in math that are not just mind boggling,but also so difficult that unless you can singlehandedly crack problems that haven't been solved for centuries, you'd need a support from someone more senior. Those more seniors most likely will be found at good universities teaching and researching the subject.

"Math is the purest form of art humans can produce."

Curious, what makes you say this? Not that I strictly disagree.

Math is no art, its structure and logic severely limits what one can imagine or do.

> but I do have bookcases of read and pending math books in the living room.

That doesn't really tell me much.