Some guy on slashdot asked how to improve his intelligence. I thought that this was a pretty well-thought-out response. "My advice is to study math and the sciences.

Intelligence is predictability

"Not many people understand how rare it is to really, really know something."
-Richard Feynman

If I could ACCURATELY predict the stock market, weather patterns, or the lottery -- would you call that intelligence? If I could quickly tell you the final result of any given set of initial conditions -- would you call that intelligence?

Intelligence is predicatability. People may be impressed by philosophers and musicians, however when it comes to raw brainpower, never look past mathematics and the hard sciences. Predicitability is key. Anyone can collect stamps. Anyone can observe. Most people can describe. However ask for an uncanny and accurate prediction and the room becomes silent.

I've found that studying mathematics and science has improved my ability to understand history, the humanities, and art. You learn to quantify things in science. When you study physics you learn what really knowing something means. You learn about the limits of knowing what you can know. You can only quantify so much. The question is how much can we actually quantify?

"Everything should be made as simple as possible, but no simpler."
-Albert Einstein

Reasoning is basic symbolic manipulation

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
-Bertrand Russell

Reasoning is basic symbolic manipulation. Even Aristotle believed this. Look at the syllogistic form. A tautology is a valid line of reasoning. Admittedly, any attempt to formalize inductive reasoning is as weak as formalizing probability itself.

Intelligence is about encoding mechanisms. When you make a mapping from the real world to a rigourous set of rules or you merely compare sets of rules, you are finding a way to encode one system in terms of another. Thus the application of analytical geometry to our (observed) real space, is an encoding of real world geometry into algebraic equations. Any description in one has a signifigant result in the other.

Teach yourself

You've got to teach yourself. Frankly, even Havard won't make the dumb smart, it will only make them educated. Just having the ability to break down information and understand it on your own is a skill. You've get to be able to solve problems on you're own. Don't just stare at the problem. Play with it. Do something. Even if it's tedious. You'd be suprised at how just hacking away at a piece of it can help you solve a problem. Heck, I'm probably preaching to the choir here.

"Don't let school get in the way of your education."
-Mark Twain (or Ben Franklin or somebody else...)

Give me a man who is mathematically mature and physcially intuitive and I will give you a genius. Genius is merely a social measurement of intelligence. Whose to say if Einstein was smarter than Hilbert. Was Godel smarter than Russell? Frankly, most of these parlor discussions are nothing more than pure bovine fecal matter. Don't obsess about how intelligent other people think you are. Frankly, if you're really smart, you will get two responses, comraderie or fear. Intelligent people will seek your company. Insecure people will tell you that you are foolish or ignorant only because they fear you actually know more. Intelligence is part performance and part stubborn confidence that you can figure something out by shear intellectual will. Of course, proving that you are a genius or even a genius in a world of geniuses is tough. However, I will leave that exercise to the reader."