School children and students who love God should never say: “For my part I like mathematics”; “I like French”; “I like Greek.” They should learn to l… - William Rowan Hamilton

Mathematics lays the foundation of all the ex­act sciences. It teaches the art of combining num­bers, of calculating and measuring distances, how to solve problems, to weigh mountains, to fathom the depths of the ocean; but gives no directions how to ascertain the existence of a God.

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.

Trying to solve real-world problems, researchers often discover that the tools they need were developed years, decades or even centuries earlier by mathematicians with no prospect of, or care for, applicability.