Is mathematics discovered or created?
HallsofIvy said:Mathematical theorems are created when we choose the axioms for the mathematical system. Of course, what statements are theorems (are provable in that system) is not immediately obvious ("emergent properties" is a good phrase to use here). We "discover" the theorems when we prove them.
opticaltempest said:Is mathematics discovered or created?
That reminds me of a quote I liked.selfAdjoint said:We seem to "find" the theorems in our heads as potential truths and then prove them by creating chains of logically interrelated statements.
(Also spelled Carl Kerenyi.)Karl Kerenyi began his 1976 English language translation of Dionysus with this passage:
"The interdependence of thought and speech makes it clear that languages are not so much a means of expressing truth that has already been established as means of discovering truth that was previously unknown. Their diversity is a diversity not of sounds and signs but of ways of looking at the world."