At 6/14/10 05:00 AM, citricsquid wrote: school is not about teaching you things, it's about teaching you how to learn.
It's not. The only thing it teaches is to sit on your ass and take bullshit. It might be appropriate preparation for many for what they're going to be doing the rest of their life, but it has nothing on real learning.
The things you do in your free time are learning.
At 6/14/10 07:08 AM, citricsquid wrote: isn't the difference that math is "absolute". It's based on a few absolute principles
These principles are called axioms. To prove things in math, you need to take a set of axioms from which you can compose theorems, the axioms comprise a theory, and theorems are truths that can be proven within the theory. Theories are thus like objects that you can compare to see what difference the difference in their axioms makes.
Up till the twentieth century, mathematicians were looking for the 'ultimate' set of axioms that could be used to prove all truths. The theory would thus be 'complete'. They also had to take care not to accidentally include an axiom that would allow contradictory truths to be derived from the theory, because this would make the theory 'inconsistent'.
Then Godel used arithmetic to prove that there is no consistent complete theory. This led to a high suicide rate among mathematicians in the thirties.
But thus the entire point is that there are no 'absolute principles'. So there isn't an ultimate reason for 1+1=2, but you need to adopt a theory to work with symbols, and with any reasonable theory the equality would be a fact.
And there are more interesting questions in math, like P versus NP and the Curry-Howard correspondence. Give me your best guess about those and I'll explain them too. :p