Have you ever taught yourself something complicated? Books can be read and comprehend and applied without paying tuition and yes sometimes you will find you need to read another book first before continuing. There are plenty of people who can do this just fine, maybe you have a different learning style but don’t assert that on everyone else.
Reading a book and thinking you understand the material is not the same thing as understanding the material. If you randomly pick a bunch of people who claim to have self taught college level mathematics and gave them the corresponding MIT exams I bet most of them would fail. If it is a higher level course I'd bet not a single one of them would pass since the things they misunderstood compounds as they get deeper down into abstractions.
Of course it is possible, a few people throughout history have done it, but it is rare enough that I would claim that anyone who thinks they did are deluding themselves unless they can come up with further proof.
To quote my prior comment, this basically says it takes more than reading. But reading is the root of it. These days “reading” encompasses everything from books, internet, and even YouTube style videos. Basically individual leaning content.
It’s very possible if you’re motivated and put in the time. College is forced motivation.
You can't apply maths as a test for it, you need someone who can tell you when you are wrong. It is not easy like a program crashing or an api returning an error, all errors when doing maths are entirely silent.
Lets take an example from the subject at hand, series in calculus: we want to prove that the sum of a series converges, how to you verify the proof without an instructor? Check that it is the same as the book? Most likely it wont be the same, proofs can come in many different ways. So either students start discarding their correct solutions thinking they are wrong or they fail to discard wrong solutions. Either case they fail to fully grasp the material.
You need to be a genius to properly root out all the errors in your head on your own, doesn't matter how many videos or books or tutorials you go through they can't evaluate your creative solutions like a real person can. Of course the need for instructors mostly disappear as you reach mathematical maturity, but to get there without help is extremely hard.
