Can you self-teach yourself Mathematics?

Question

If you are not a natural genius, can you teach yourself Mathematics (through textbooks) enough to make a successful mathematical career?

Answer 1

The answer to this question has a simple answer: Maybe. The ability to learn mathematics independently from textbooks depends on (1) your willingness do so, and (2) how well you can read mathematics. Many students who take introductory college math courses (i.e., College Algebra, and Calculus) learn new concepts primarily by attending lectures, and usually avoid reading any kind of textbook. And if students accompany their lectures with a ton of practice problems, they usually get good test scores, and end up never reading a math textbook (unless they're majoring in math). The issue that arises is with this that these students probably don't fully grasp the concepts behind the problems they are working. In order to obtain a true understanding of a mathematical concept, read a textbook about it. But know that reading mathematics is not like reading literature. You have to read slowly and ensure that you fully understand each statement. Work examples as you read them to make sure you understand each step. It's also important to know that Mathematical statements are very compact. Most of the most important and influential theorems in mathematics can be stated in one or two sentences. So if you feel like it takes you "too long" to read math textbooks, you're wrong. So to summarize: Yes, it is possible for anyone to learn mathematics on their own through textbooks. But it is a very time consuming, and frustrating endeavor. And if you don't have the passion and dedication to learn mathematics, you probably won't learn it. Especially not on your own. If you really want to become good at mathematics on your own, read some math books, and do a lot of practice problems.

As to making a successful career in mathematics, I don't think many will hire you without a degree.