During his career in mathematics, George Green developed some of the most important ideas in the area of mathematical physics. Chief among these was the development of potential function, subsequently used to describe electrical and magnetic fields as well as the energy present in some mechanical systems. His contributions are even more remarkable because he had virtually no formal schooling, rarely had time to devote to research, and was largely self-taught in mathematics.
Green was born to an English baker, also named George Green. His formal schooling was minimal, consisting of only a single year at age eight. However, it is thought that a mathematics student at nearby Cambridge, John Coplis, must have tutored Green in not only mathematics, but French as well. French was important because of the prominence held by French mathematicians at that time; many important papers were written in French and the new "French style" of mathematics was considered an important advance.
For the next several years, Green studied math on his own in the top floor of his father's grain mill, where he worked full-time. In addition to his duties in the family mill, Green was also the father of seven children, although he never formally married their mother. During this time, too, Green's parents died, leaving him the mill. In spite of his lack of formal education and his sketchy background in mathematics, Green published what was to become one of the most important mathematical works of his century and, arguably, of any century.
Green's Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism was published by subscription in 1828. By chance, one of the subscribers understood the importance of Green's work, though he did not understand the mathematics itself. Sir Edward Bromhead offered to send future papers of Green's to any of a number of scientific bodies for publication, an offer that Green eventually accepted. Between 1830, when they first met in person, and 1834, Green and Bromhead met regularly and Green wrote three major papers, two on electricity and one on hydrodynamics. All three were published, though received little attention.
During this time Green consistently under-rated his abilities because of his lack of formal education. He simply did not realize the importance of his work. Finally, at age 40, Green enrolled in Cambridge as an undergraduate, completing his degree in 1837. Following his graduation, Green continued his work on hydrodynamics, writing two papers that were published in 1838 and 1839. Around this time he was awarded the Perse fellowship at Cambridge. Unfortunately, his tenure was to be short as he fell ill in 1840, dying just a year later of an unknown illness. His obituary, printed in the local newspaper, stated, "Had his life been prolonged, he might have stood eminently high as a mathematician." Ironically, at the time of his death even Green did not apprehend the importance of his work, or the recognition that would later come to him.
Green's work was not fully appreciated during his life. However, shortly after his death William Thomson (1824-1907), later Lord Kelvin, came across a reference to one of Green's papers. Tracking this down four years later, Thomson realized the importance of the work. He shared copies of the paper with Joseph Liouville (1809-1882) and Jacques Sturm (1803-1855), both of whom shared his excitement over the work. Thomson republished Green's paper, making it accessible to James Clerk Maxwell (1831-1879) and others who could use and build upon the work of this unknown, largely self-educated son of a miller.
P. ANDREW KARAM