Perhaps the Pythagoreans were the first to suggest that “at its deepest level, reality is mathematical in nature”. Although by today's standards their mathematical tools were limited, they found interesting numerical patterns in musical harmonies as well as in geometric figures.

The flourishing of science in Europe during the Renaissance was made possible by increasing knowledge of mathematics. Galileo echoed Pythagoras when he observed that the laws of nature are “written in the language of mathematics”.

It is surprising how often branches of pure mathematics that seem to have no application to the real world turn out later to be very important in physics or other fields. Eugene Wigner described this as “the unreasonable effectiveness of mathematics in the natural sciences”, in his famous 1960 essay.