Josiah Willard Gibbs (1839-1903)
Willard Gibbs was an American physical chemist. He also contributed to mathematics as one of the founders of vector analysis.
Gibbs' scientific career can be divided into four phases. Up until 1879, he worked on the theory of thermodynamics. From 1880 to 1884, he worked on the field of vector analysis. From 1882 to 1889, he worked on Optics and the theory of light. After 1889, he worked on textbooks on statistical mechanics.
Gibbs was born in New Haven, Connecticut, where his father was a professor of sacred literature at Yale University's Divinity School. (Though his father was also named Josiah Willard, he is not referred to as "Josiah Willard Gibbs, Jr.") Gibbs attended Yale College of Yale University, receiving prizes in mathematics and Latin. He graduated, high in his class, in 1858, received his Ph.D. there in 1863—one of the first doctorates granted in the United States—tutored Latin and natural philosophy there, and then left for three decisive years in Europe.
Up to that time Gibbs had shown interest in both mathematics and engineering, which he combined in his dissertation "On the Form of the Teeth of Wheels in Spur Gearing." The lectures he attended in Paris, Berlin and Heidelberg, given by some of the greatest men of the day, changed him once and for all. In 1871, two years after his return from Europe, he became Yale's first Professor of Mathematical Physics. He had not yet published any papers on this subject. For nine years he held the position without pay, living on the comfortable inheritance his father had left; only when Johns Hopkins University offered Gibbs a post did Yale give him a small salary.
Gibbs never married. He lived out a calm and uneventful life in the house where he grew up, which he shared with his sisters. He was a gentle and considerate man, well-liked by those who knew him, but he tended to avoid society and was little known even in New Haven. Nor was he known to more than a few of the world's scientists—partly because his writings were extremely compact, abstract and difficult. As one of Gibbs' European colleagues wrote, "Having once condensed a truth into a concise and very general formula, he would not think of churning out the endless succession of specific cases that were implied by the general proposition; his intelligence, like his character, was of a retiring disposition." The Europeans paid for their failure to read Gibbs: A large part of the work they did in thermodynamics before the turn of the century could have been found already in his published work.
Gibbs' important 1873 papers were Graphical Methods in the Thermodynamics of Fluids and A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces. In 1876 Gibbs published the first part of the work for which he is most famous On the Equilibrium of Heterogeneous Substances, publishing the second part of this work in 1878.
Gibbs' chief scientific papers appeared in the Transactions of the Connecticut Academy of Arts and Sciences. The articles were expensive to set in type because of their length and their wealth of mathematical formulas, so funds were raised by subscription from Yale professors and New Haven businessmen, few or none of whom could understand the publication they were subsidizing. The Connecticut Academy's Transactions were little read, but Gibbs tried to make his results known by mailing many reprints and by publishing a summary elsewhere.
In these papers Gibbs' starting point for analyzing a system was the state of equilibrium, which (as he pointed out) is characterized by a maximum in the system's entropy. This principle, he noted, was already known to physicists, but "its importance does not appear to have been appreciated. Little has been done to develop the principle as a foundation for the general theory of thermodynamic equilibrium." He proceeded to correct this situation, demonstrating for the first time the uses of the differential relationship in a system between energy U, pressure P, volume V, temperature T, and the entropy S, the last a quantity then scarcely understood: dU = TdS - PdV. Adding terms to allow for variations in the chemical constitution of the system, he derived an astonishing variety of consequences. Many phenomena which had never been within the domain of thermodynamics were now annexed by this equation, including elastic and surface phenomena, changes of phase, and a great part of chemistry.
Once this was completed Gibbs turned to another subject. In 1892 he wrote Lord Rayleigh with characteristic modesty, "Just now I am trying to get ready for publication something on thermodynamics from the a priori point of view, or rather on 'Statistical Mechanics' . . . I do not know that I shall have anything particularly new in substance, but shall be contented if I can so choose my standpoint (as seems to me possible) as to get a simpler view of the subject." Ten years later this work resulted in a classic book which put statistical mechanics on a new and more general basis.
By the turn of the century Gibbs was becoming fairly well known, as much for his vigorous and partisan defense of the form of vector notation which is now standard as for his more basic work. But aside from summers spent hiking in the mountains, he continued to the end of his days to spend nearly all his time in work or in walking about the few blocks that included his home and his college.
In 1901, at the age of 62, Gibbs published a book called Elementary Principles in Statistical Mechanics (Dover, New York). It was remarkable in several ways. First, it had as a subtitle The Rational Foundation of Thermodynamics. Gibbs chose this subtitle because he knew his theory did not agree with experiments, as he emphasized in the preface to the book. Yet he believed there were no other possible rational basis to thermodynamics. Second, the style of writing of the book has an elegance akin to a long poem, which is quite unique in the history of physics. Third, it was to become the fundamental basis of twentieth century equilibrium statistical mechanics. A year before Einstein's death in 1955, he was asked who were the most powerful thinkers he had known. He replied, "Lorentz", and added, "I never met Willard Gibbs; perhaps, had I done so, I might have placed him beside Lorentz".