Mathematics as the language of Nature - A Historical View

Abstract

We review in historical terms the changing relationship between mathematics and modern science over the past four centuries. Focussing on physics, we start with the establishment of the Galilean Newtonian tradition in science. Two Phases in the mathematics – physics relationship are described : an earlier one with progress in each going hand in hand with the other ; and a later one with new mathematical concepts finding use in physics after a faw decades. Instances of mathematicla formulations of new physical laws coming well before physical understanding are highlighted. Some lessons we can draw about the roles of mathematics in the description of physicalphenomena, and ideas about the nature of mathematics itself, are discussed against the background of Kantian ideas on the natur of human knoeledge. The depth of the connection between the two is emphasized and illustrated with quotations from the masters.