Recopilación de resoluciones del problema de Basilea

Abstract

The Basel Problem consists in finding if, actually, the sum of inverse squares of the natural numbers converges and to what value. This problem was first solved by Euler but numerous proofs have been obtained later. We compile some of its most important proofs and show the versatility of approaches to the Basel Problem by pointing out the potential of certain theories (particularly, the Fourier series theory), the most direct and unsuspected proofs, as well as the bridges that are built between various areas of mathematics.