Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers. The method can be extended to prove statements about more ...

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

Metamathematics investigates the structure and limitations of mathematical theories, with proof theory focusing on the nature of formal proofs and the principles that govern them. In the context of ...