Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself

Mathematics consists in proving the most obvious thing in the least obvious way.

Mathematics is not a spectator sport!

In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.

You should not put too much trust in any unproved conjecture, even if it has been propounded by a great authority, even if it has been propounded by yourself. You should try to prove it or disprove it.

The principle is so perfectly general that no particular application of it is possible.

If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.