# Josiah Willard Gibbs : biography

## Influence

Gibbs’s most immediate and obvious influence was on physical chemistry and statistical mechanics, two disciplines which he greatly helped to found. During Gibbs’s lifetime, his phase rule was experimentally validated by Dutch chemist H. W. Bakhuis Roozeboom, who showed how to apply it in a variety of situations, thereby assuring it of widespread use. In industrial chemistry, Gibbs’s thermodynamics found many applications during the early 20th century, from electrochemistry to the development of the Haber process for the synthesis of ammonia.

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 Planck’s law for quantized black-body radiation. That work was based largely on the thermodynamics of Kirchhoff, Boltzmann, and Gibbs. Planck declared that 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 statistical ensembles, as presented in his 1902 textbook, has had a great 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:

Gibbs’s early papers on the use of graphical methods in thermodynamics reflect a powerfully original understanding of what mathematicians would later call "convex analysis",Wightman 1979, pp. x–xxxiv including ideas that, according to Barry Simon, "lay dormant for about seventy-five years". Important mathematical concepts based on Gibbs’s work on thermodynamics and statistical mechanics include the Gibbs lemma in game theory, the Gibbs inequality and Gibbs algorithm in information theory, as well as Gibbs sampling in computational statistics.

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".Seeger 1974, p. 18 De Forest credited Gibbs’s influence for the realization "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.