The Intimate Relation Between Mathematics and Physics
Overview
Since the 1960s physics has seen a rebirth of the use of advanced mathematics. Much of this revival occurred after the study of black holes was greatly expanded in the 1960s and 1970s by the English scientists Stephen Hawking (1942- ) and Roger Penrose (1931- ). In the 1980s physicists' 10-dimensional superstring theories received another mathematical boost from tools developed by Edward Witten (1951- ) and others.
Background
Physics and mathematics have always enjoyed a close relationship, beginning in the Renaissance with Johannes Kepler's (1571-1630) 1609 discovery of the three laws of planetary orbits. In 1687Isaac Newton (1642-1727) introduced the theory of gravity. James Clerk Maxwell (1831-1879) was able to unify the forces of electricity and magnetism in 1865 with the theory of electromagnetism. In the twentieth century mathematical theories from the fields of geometry were instrumental in constructing Albert Einstein's (1879-1955) theory of general relativity as well as in the later development of superstring theory. All of these theories have been predicated upon the prior development of mathematical techniques that had been invented for pure and applied purposes.
In the late seventeenth century Isaac Newton could not have developed the theory of gravity without calculus, a set of mathematical techniques he had developed for studying rates of change.
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