The reason of self-learning mathematics.

Question

I know there are lot of people that are self-learners. But why? What is the reason? I want to know that because this is my last year in university, and I don't know what I will do then but I love maths and I don't want to leave them. So I don't know if keep on studying them at university, or continue studying other thing like data science but I don't want to stop studying PDE, FA, Differential Geometry, Algebra or Analysis for example. What is the reason for studying mathematics on your own? By pleasure? because universities aren't good enough? what is the point? I'm not saying how to do an integral or something like that, I mean mathematic (abstract maybe) theory. I don't know anybody that are doing it. I'm a little lost. Greetings and thank you in advance, Miguel.

Answer 1

This was initially a comment.

I'm not sure if this is the place to ask such a question, but I will answer it anyways. Don't worry about what other people do. People are different in terms of how they make progress in a rigorous field like mathematics. That shouldn't really discourage you.

That being said, if you like mathematics, wouldn't you want to learn more on your own ? The truth is that many abstract topics tend to take a little more time to learn, and a lecture may not be enough to soak it in. This is true for me, and I am sure this is true for many other students or people in the field. Hence, it would be in your best interest to study on your own if you want to fully understand more difficult topics. As a matter of fact, the process of learning more and investigating is precisely what mathematical research is all about.

By being a user on Stack Exchange, you automatically place yourself in a position to learn more mathematics. Witness the diversity of questions and answers that pop up at this very second. By writing questions or answers, or by observing other people's questions or answers, you can learn more advanced topics as well as learning to communicate your knowledge to others.

Answer 2

I decided to answer because perhaps I can relate? I started in math in school because it is what I would call today, decidable or at least I perceive it fundamentally should be. And at least early on it was, compared to other areas of academia in which it is often up to the professors opinion the student. I liked that my answer could be right or wrong regardless of my attributes.

Coming up through school there was a very natural progression I thought through multivariable calculus. There was no obscure motivation and why should there be?

Then came along algebra. Everything changed drastically and wasn't even clear what the motivation was? This was difficult time for me. With hind site I believe it could be taught much better, however I'm fresh from having learned whilst my professor a 30 year tenured professor from university of Chicago, who's professors had categorized groups in the sixties.

Unfortunately it had somehow turned itself into just another course where a good impression and mimicking what had been taught was the way. My underlying concept of what I thought math should be was no longer useful and in some cases seen as annoying to others when outwardly expressed.

Math education I believe has been grouped with other subjects and taught to be taught like other subjects, often professors coming from other fields.

I ounce had a conversation with a berkly professor who told me that I got the material while others didn't and should be grateful and more studious with homework and studying. The conversation was about if so.e people get it and others don't, I realize now that wasn't what was meant but I still hold on that a subject should be able to be taught with enough logical inductive steps that just about anyone should get it. With many higher level subjects this is hardly the case. Perhaps it is related to millennium prize question about equivalence of two well known types of problems?

Anyways long story short, I never went on to grad school unfortunately, partly due to my changing views on universities and society and it generally being a poor place for learning math. So maybe, self learning is the best way to learn math?