In the 18th and 19th centuries, Newton’s mathematical description of motion using calculus and his model were extended very successfully to the emerging science and technology of electromagnetism. Calculus evolved into Classical Field theory.

Once electromagnetic fields were thoroughly described using mathematics, many physicists felt that the field was finished, that there was nothing left to describe or explain

Then the electron was discovered, and particle physics was born. Through the mathematics of quantum mechanics and experimental observation, it was deduced that all known particles fell into one of two classes: bosons or fermions.

The discovery of light travelling at a fixed speed in vacuum and the mathematics that Einstein developed to describe it and model it in his Special Theory of Relativity, when combined with the later development of quantum mechanics, gave birth to the rich subject of relativistic quantum field theory.

But Einstein then extended his Special Theory of Relativity to encompass Newton’s theory of gravitation, and the result, Einstein’s General Theory of Relativity, brought the mathematics called differential geometry into physics.

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