George Green (14 July 1793 – 31 May 1841) was a British mathematical physicist. Despite being almost entirely self-taught, having received only about one year of formal schooling as a child, between the ages of 8 and 9, Green made a number of key contributions to mathematical physics. He is now best remembered for his Essay on electricity and magnetism of 1828, in which he introduced an early version of Green's theorem in vector calculus, the notion of potential functions as currently used in physics, and a method of solving differential equations called Green's functions. This paper formed the foundation for the work of later scientists such as William Thomson (later Lord Kelvin), among many others. His work on potentials ran parallel to that of Carl Friedrich Gauss.
Green also studied hydrodynamics, acoustics, and optics.
Early life
Green was born and lived for most of his life in the English town of Sneinton, Nottinghamshire, now part of the city of Nottingham which then had a population of around 30,000. He was baptized on 14 July 1793.
Nottingham Subscription Library
When Green was thirty, he became a member of the Nottingham Subscription Library, then the intellectual heart of the town. This library was likely the main source of Green's advanced mathematical knowledge, giving him access to the Philosophical Transactions of the Royal Society, among other scientific journals. While foreign journals were not available, the Transactions did mention their contents, which allowed Green to obtain reprints directly from their authors. He then served as headmaster of the Nottingham Free Grammar School 1806–1819, and lived in the same neighbourhood as Green and his family. Toplis was an advocate of the continental school of mathematics, and fluent in French, having translated Pierre-Simon Laplace's celebrated work on celestial mechanics (Traité de mécanique céleste). The possibility that Toplis played a role in Green's mathematical education would resolve several long-standing questions about the sources of Green's mathematical knowledge. In the Preface to his 1814 translation of Laplace, Toplis recommended the works of French mathematicians Joseph-Louis Lagrange, Adrien-Marie Legendre, and Sylvestre François Lacroix. When Green published his Essay, it was sold on a subscription basis to 51 people, many of whom were members of the Nottingham Subscription Library, the same one Bromhead went to. The last three were studying the Schrödinger equation in quantum mechanics. However, the Liouville–Green approximation is now commonly known as the WKBJ method. In modern language, this method involves the use of an asymptotic series.
In 1845, four years after Green's death, Green's work was rediscovered by the newly graduated William Thomson (then aged 21), later known as Lord Kelvin. Thomson became aware of Green's Essay after reading the aforementioned paper by Murphy, but to his dismay, could not find any Cambridge booksellers who even remembered it. Richard Feynman's formulation of QED in terms of path integrals and his diagrams also employed Green's functions, which, in the context of particle physics, are known as Feynman propagators. In 1985, Green's Mill, in Sneinton, Nottingham was restored to working order. It now serves both as a working example of a 19th-century windmill and as a museum and science centre dedicated to Green.
His work and influence on 19th-century applied physics had been largely forgotten H. Gwynedd Green (no relations), a member of the Department of Mathematics at the University of Nottingham, wrote a biography of him in 1945. Mary Cannell published a more substantial account in 1993; the second enlarged edition appeared in 2001. and within proximity to the memorial plaques of Michael Faraday and James Clerk Maxwell.