[MtnClimber]

It is amazing that new mathematical methods continue to be developed.

[Secret Agent Man]

Discovered. God already developed them. We discover them.

[Do the math]

My paper in analytic geometry has just been accepted, just need to make a few minor changes. After solving that particular problem, it made me think of at least ten new problems. Math is a never ending story. Number theory , to me, is the most difficult type of mathematics. I love mathematics.

[LibWhacker]

Gödel's incompleteness theorem: no consistent system of axioms whose theorems can be listed by an "effective procedure" (i.e., an algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. (Wiki)

Furthermore, given there are some theorems that are so difficult they will in all likelihood never be proven -- even though they are true -- new mathematical methods will continue to be developed for as long as men are alive.