This is the title of a talk given at the Harvard mathtable on Sep. 18, 2018.
David Hilbert's "Entscheidungsproblem" asks for an algorithm to prove or disprove any mathematical statement. The non-existence of such an algorithm was proven independently by Church and Turing. This is often interpreted as meaning that there is no streamlined method to prove something: it takes hard work and creativity... Or does it? What did Church and Turing precisely prove? Could we imagine a hypercomputer capable of performing infinitely-many steps in a finite time? Could we build such a machine, or at least come close? I will discuss these questions and more.