George Green: A Singular Life
George Green is listed in most references as a mathematical physicist. This would certainly surprise many of George Green's peers. Green was a miller, and worked long hours at the wind-powered mill that his father had built. In 1828, while working as a miller, Green published his Essay "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism," which was sold to 51 people who most likely could not understand it. In the preface of his Essay Green wrote:
"Should the present Essay tend in any way to facilitate the application of analysis to one of the most interesting of the physical sciences, the author will deem himself amply repaid for any labour he may have bestowed upon it; and it is hoped the difficulty of the subject will incline mathematicians to read this work with indulgence, more particularly when they are informed that it was written by a young man, who has been obliged to obtain the little knowledge he possesses, at such intervals and by such means, as other indispensable avocations which offer but few opportunities of mental improvement, afforded."
In a few years, this Essay stunned the intellectual community of England and became one of the most important works in many areas of physical sciences. Why was the publication such a shock to those who later discovered it? There are three reasons:
1) George Green was totally unknown, and for good reason -- as far as we can tell, when he published this Essay, he had attended no school since he was 9 years old!
2) Green used the term "mathematical analysis" in the title, which suggested (correctly) that he was using mathematical techniques entirely uncommon in England at the time. The so-called "continental notation" for calculus was very unpopular in England, and everyone else in the country who knew this way of doing mathematics had learned it in the mainland of Europe. It is thus very confusing how Green, who essentially never left his mill, could have learned it.
3) The Essay is simply brilliant. In it, Green introduces a way of determining the electric potential inside a charged sphere. That is, he solves a differential equation by relating it to the values certain integrals take on the boundary of a sphere. In essence, Green showed that to understand what was happening inside the sphere, it was sufficient to understand what was happening on its boundary.
Unfortunately, Green's life is not so easily understood. Despite knowing the surface details about his lack of education and means of employment, we don't have any further insight into HOW Green was able to accomplish what he did. Perhaps it will always remain a mystery, but in analyzing the impact of Green's Essay on a broad area of mathematical physics one must agree with the conclusion that theoretical physicist Julian Schwinger made in his article about George Green The Greening of Quantum Field Theory: George and I,
"So ends our rapid journey through 200 years. What, finally, shall we say about George Green? Why, that he is, in a manner of speaking, alive, well, and living among us."