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 ...

A simple, step-by-step breakdown of two “perfect” math proofs. But which prime number is p? It must be on our list of primes, because our list is complete. But it also can’t be on our list of primes, ...

Let us assume what most mathematical readers would take for granted anyway: There are mathematical objects such as numbers and functions and there are objective facts about these objects, such as 3 < ...

PROOFS are the currency of mathematics, but Srinivasa Ramanujan, one of the all-time great mathematicians, often managed to skip them. Now a proof has been found for a connection that he seemed to ...