Five Contributions to Natural Philosophy

Description

In the 17th and 18th century, mathematics and physics were not the separate specialties that they are today, and Natural Philosophy was the term used for the endeavor to understand nature by using conceptual mathematical tools. Perhaps the most important scientific work of that era is Newton’s Philosophiae Naturalis Principia Mathematica, published in 1687. He invented differential calculus, with new mathematical concepts, a new terminology, and new notations, which made possible a concise formulation of the laws of particle mechanics now named after him. In the 1960’s, Clifford Truesdell tried, and to some extent succeeded, to revive not only the term Natural Philosophy but also the spirit behind it. He was the driving force behind the founding, in 1963, of the Society for Natural Philosophy, which still exists today. (I was one of the founding members.) Much of my own work has been in the spirit of Natural Philosophy. In recent years, many of the mathematicians working in the field of continuum physics have de-emphasized this spirit and have concentrated more and more on obtaining existence theorems and other “results” rather than analyzing basic concepts. I have been out of step with this trend, but I have not been completely idle. This collection presents some of the ideas that I have developed in the past 10 years or so.