Introduction

"How to learn math and physics" — the title is deliberately provocative. Everyone has to learn their own way. I don't know how you should learn math and physics. But presumably you came here looking for advice, so I'll give you some.

My advice is aimed at people who are interested in fundamental theoretical physics and the math that goes along with that. (By "fundamental" physics I mean the search for the basic laws concerning matter and the forces of nature.) If you want to do experiments instead of theory, or other kinds physics like condensed matter physics and astrophysics, or math that has nothing to do with physics, my advice will be of limited use. You should still learn the basics I mention here, but after that you'll have to look elsewhere for suggestions.

Learning math and physics takes a whole lifetime. Luckily, it's a lot of fun... if you have a reasonably patient attitude. A lot of people read pop books about quantum mechanics, black holes, or Gödel's theorem, and immediately want to study those subjects. Without the necessary background, they soon become frustrated — or worse, flaky.

It can be even more dangerous if you want to plunge into grand unified theories, or superstrings, or M-theory. Nobody knows if these theories are true! And it's hard to evaluate their claims until you know what people do know.

So, especially when it comes to physics, I urge you to start with slightly less glamorous stuff that we know to be true — at least as a useful approximation, that is — and then, with a solid background, gradually work your way up to the frontiers of knowledge. Even if you give up at some point, you'll have learned something worthwhile.

This webpage doesn't have lots of links to websites. Websites just don't have the sort of in-depth material you need to learn technical subjects like advanced math and physics — at least, not yet. To learn this stuff, you need to read lots of books. I will list some of my favorites below, and also some you can get free online.

But, you can't learn math and physics just by reading books! You have to do lots of calculations yourself — or experiments, if you want to do experimental physics. Textbooks are full of homework problems, and it's good to do these. It's also important to make up your own research topics and work on those.

If you can afford it, there's really nothing better than taking courses in math and physics. The advantage of courses is that you get to hear lectures, meet students and professors, and do some things you otherwise wouldn't — like work your butt off.

It's also crucial to ask people questions and explain things to people — both of these are great ways to learn stuff. Nothing beats sitting in a cafe with a friend, notebooks open, and working together on a regular basis. Two minds are more than twice as good as one!

But if you can't find a friend in your town, there are different ways to talk to people online. In all cases, it's good to spend some time quietly getting to know the local customs before plunging in and talking. For example, trying to start a rambling discussion on a question-and-answer website is no good. Here are some options:

There are also lots of interesting blogs and free math books online.

Finally, it's crucial to admit you're wrong when you screw up. We all make tons of mistakes when we're learning stuff. If you don't admit this, you will gradually turn into a crackpot who clutches on to a stupid theory even when everyone else in the world can see that it's wrong. It's a tragic fate, because you can't even see it's happening. Even bigshot professors at good universities can become crackpots once they stop admitting their mistakes.

To avoid looking like a fool, it's really good to get into the habit of making it clear whether you know something for sure, or are just guessing. It's not so bad to be wrong if you said right from the start that you weren't sure. But if you act confident and turn out to be wrong, you look dumb.

In short: stay humble, keep studying, and you'll keep making progress. Don't give up — the fun is in the process.