||Number theory is the branch of pure mathematics dealing with the integers, functions on the integers and related matters. As a body of mathematical knowledge, number theory is interesting for several reasons: for instance, because many of its statements are very simple but very hard to prove, often seeming to require methods of surprising depth and complexity. (Fermat's Last Theorem, the Goldbach conjecture and the Twin Primes conjecture are famous examples.) As an axiomatic system, arithmetic and its fragments and extensions are primary objects of study for logicians. As mathematical objects, the integers are focal points of various debates in metaphysics and epistemology: about the existence of numbers and their relationship to sets, the a priori vs. a posteriori status of arithmetic, and the origins and nature of numerical cognition, to name a few.