Josiah Willard Gibbs - Influence

Influence

According to American experimental physicist and Nobel laureate Robert A. Millikan,

Gibbs lives because, profound scholar, matchless analyst that he was, he did for statistical mechanics and for thermodynamics what Laplace did for celestial mechanics and Maxwell did for electrodynamics, namely, made his field a well-nigh finished theoretical structure. — R. A. Millikan, 1938

Gibbs's most immediate and obvious influence was on physical chemistry and statistical mechanics, two disciplines which he greatly helped to found. When Dutch physicist J. D. van der Waals received the 1910 Nobel Prize "for his work on the equation of state for gases and liquids" he acknowledged the great influence of Gibbs's work on that subject. Max Planck received the 1918 Nobel Prize for his work on quantum mechanics, particularly his 1900 paper on the quantization of black-body radiation (see Planck's law). That work was based largely on the thermodynamics of Kirchhoff, Boltzmann, and Gibbs. According to Planck, Gibbs's name "not only in America but in the whole world will ever be reckoned among the most renowned theoretical physicists of all times."

The first half of the 20th century saw the publication of two influential textbooks that soon came to be regarded as founding documents of chemical thermodynamics, both of which used and extended Gibbs's work in that field: these were Thermodynamics and the Free Energy of Chemical Processes (1923), by Gilbert N. Lewis and Merle Randall, and Modern Thermodynamics by the Methods of Willard Gibbs (1933), by Edward A. Guggenheim. Under the influence of Lewis, William Giauque (who had originally wanted to be a chemical engineer) went on to become a professor of chemistry at Berkeley and won the 1949 Nobel Prize in Chemistry for his investigations into the properties of matter at temperatures close to absolute zero, studies guided by the third law of thermodynamics.

Gibbs's work on ensembles and on the ergodic hypothesis, as presented in his 1902 textbook on statistical mechanics, has had a considerable impact in both theoretical physics and in pure mathematics. Initially unaware of Gibbs's contributions in that field, Albert Einstein wrote three papers on statistical mechanics, published between 1902 and 1904. After reading Gibbs's textbook (which was translated into German by Ernst Zermelo in 1905), Einstein declared that Gibbs's treatment was superior to his own and explained that he would not have written those papers if he had known Gibbs's work. According to mathematical physicist Arthur Wightman:

It is one of the striking features of the work of Gibbs, noticed by every student of thermodynamics and statistical mechanics, that his formulations of physical concepts were so felicitously chosen that they have survived 100 years of turbulent development in theoretical physics and mathematics. — A. S. Wightman, 1990

The development of vector calculus was Gibbs's other great contribution to mathematics. The publication in 1901 of E. B. Wilson's textbook Vector Analysis, based on Gibbs's lectures at Yale, did much to propagate the use of vectorial methods and notation in both mathematics and theoretical physics, definitively displacing the quaternions that had until then been dominant in the scientific literature.

At Yale, Gibbs was also the mentor of Lee De Forest, who went on to invent to the triode amplifier and has been called the "father of radio." According to De Forest, it was thanks to Gibbs that he realized early on "that the leaders in electrical development would be those who pursued the higher theory of waves and oscillations and the transmission by these means of intelligence and power." Another student of Gibbs who played a significant role in the development of radio technology was Lynde Wheeler.

Gibbs also had an indirect influence on mathematical economics. He supervised the thesis of Irving Fisher, who received the first Ph.D. in economics from Yale in 1891. In that work, published in 1892 as Mathematical Investigations in the Theory of Value and Prices, Fisher drew a direct analogy between Gibbsian equilibrium in physical and chemical systems, and the general equilibrium of markets, and he used Gibbs's vectorial notation. Gibbs's protegé Edwin Bidwell Wilson became, in turn, a mentor to leading American economist and Nobel Laureate Paul Samuelson. In 1947, Samuelson published Foundations of Economic Analysis, based on his doctoral dissertation, in which he used as epigraph a remark attributed to Gibbs: "Mathematics is a language." Samuelson explicitly acknowledged the influence of Gibbs's classical thermodynamic methods and identified him as "Yale's great physicist."

For his part, mathematician Norbert Wiener cited Gibbs's use of probability in the formulation of statistical mechanics as "the first great revolution of twentieth century physics" and as a major influence on his conception of cybernetics. Wiener explained in the preface to his book The Human Use of Human Beings that it was "devoted to the impact of the Gibbsian point of view on modern life, both through the substantive changes it has made to working science, and through the changes it has made indirectly in our attitude to life in general."