[sweetjazz]

[ QUOTE ]
Isn't Mathematics just a series of definitions?

Aren't definitions invented, not discovered?

Those are sincere questions, not rhetorical at all.

Josh

[/ QUOTE ]

Mathematical also involves deriving consequences from definitions and axioms. For example, you can define what a prime number is. Then you can derive from this definition (and basic axioms about numbers) that there are infinitely many. This is a fact that is not a mere definition.

Most mathematicians believe that there have always been infinitely many primes, even before it was first proven (presumably by the Greeks, more specifically Euclid). Thus, they are presumably more likely to say that the infinitude of primes was discovered, not invented. Whether the notion of prime number was discovered or invented is likely to generate more debate, and I am not sure it is the right question to ask.