Alain Connes

“Connes is one of the revolutionaries of the subject (Riemann hypothesis), a benign Robespierre of mathematics to Bombieri's Louis XVI.”

“There are two fundamental sources of ‘bare’ facts for the mathematician. These are, on the one hand the physical world which is the source of geometry, and on the other hand the arithmetic of numbers which is the source of number theory. Any theory concerning either of these subjects can be tested by performing experiments either in the physical world or with numbers. That is, there are some real things out there to which we can confront our understanding.”