If you are not a natural genius, can you teach yourself Mathematics (through textbooks) enough to make a successful mathematical career?
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do you mean learn from the books? certainly sure – janmarqz Jul 12 '18 at 22:35
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4This has already been discussed: Can a chemical engineer become a self taught mathmatician? – Justin P. Jul 12 '18 at 22:35
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2I don't think you can learn math without teaching yourself. This is somewhat glib, but I mean this sincerely. – Jul 12 '18 at 22:57
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Yes, and it would help if you could get a college curriculum and course syllabi to give your learning some structure. Math careers usually require a degree. – Phil H Jul 12 '18 at 23:44
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Yes, yes, yes, yes, yes. (on a more serious note, a significant part of research is self studying the existing literature on a subject that interests you. Though some research is in a group, it would be very hard to do research without any self study capability - which comes with practice. Start practicing now, and good luck on your mathematical journey! ) – Brevan Ellefsen Jul 13 '18 at 00:16
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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.
JB071098
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1Don't forget that there is a pretty good amount of mathematics lectures available on YouTube for free, as well as resources like MIT OpenCourseware which have homeworks, tests, and projects you can do. It may be stretching the "self-taught" definition, but usually people just want to learn it without going back to (and paying for) college. You will have to read math, but it doesn't have to be your only resource! – Alex Jones Jul 13 '18 at 00:00
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1@AlexanderJ93 Absolutely. But the question was whether or not you can self teach yourself mathematics through textbooks. – JB071098 Jul 13 '18 at 00:31