Josiah Willard Gibbs

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For Josiah Willard Gibbs, Sr., see Willard Gibbs (linguist).
J. Willard Gibbs
Born February 11 1839(1839-02-11)
New Haven, Connecticut, U.S.
Died April 28 1903 (aged 64)
New Haven, Connecticut, U.S.
Residence U.S.
Nationality U.S.
Fields Physicist
Institutions Yale University
Alma mater Yale University
Doctoral advisor Gustav Kirchhoff</br>Hermann von Helmholtz
Doctoral students Edwin Bidwell Wilson</br>Irving Fisher
Known for Gibbs free energy</br>Gibbs entropy</br>Vector analysis</br>Gibbs-Helmholtz equation</br>Gibbs algorithm</br>Gibbs distribution</br> Gibbs state</br>Gibbs phenomenon
Notable awards Rumford Prize (1880) </br>Copley Medal (1901)

Josiah Willard Gibbs (February 11, 1839April 28, 1903) was an American theoretical physicist and chemist, and mathematician. One of the greatest American scientists of all time, he devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis (independently of Oliver Heaviside). It is in good part thanks to Gibbs that much of physical and chemical theory has since been exposited using vector analysis. Yale University awarded Gibbs the first American Ph.D. in engineering in 1863, and he spent his entire career at Yale.[1]

In 1901, Gibbs was awarded the highest possible honor granted by the international scientific community of his day, granted to only one scientist each year: the Copley Medal of the Royal Society of London, for being "the first to apply the second law of thermodynamics to the exhaustive discussion of the relation between chemical, electrical, and thermal energy and capacity for external work."[2] This quotation summarizes Gibbs's greatest scientific contribution.


Early years

File:A young Willard Gibbs.jpg
Gibbs in his youth.

Gibbs was the seventh in a long line of American academics stretching back to the 17th century. His father, a professor of sacred literature at the Yale Divinity School, is now most remembered for his involvement in the Amistad trial. Although the father was also named Josiah Willard, the son is never referred to as "Jr." Five other members of Gibbs's extended family were named Josiah Willard Gibbs. His mother was the daughter of a Yale graduate in literature.

After attending the Hopkins School, Gibbs matriculated at Yale College at the age of 15. He graduated in 1858 near the top of his class, and was awarded prizes in mathematics and Latin.

Middle years

In 1863, Gibbs was awarded the first Ph.D. degree in engineering in the USA from the Sheffield Scientific School at Yale. He then tutored at Yale, two years in Latin and one year in what was then called natural philosophy, now comparable to the natural sciences, particularly physics. In 1866 he went to Europe to study, spending a year each at Paris, Berlin, and Heidelberg, where he was influenced by Kirchhoff and Helmholtz. At the time, German academics were the leading authorities in chemistry, thermodynamics, and theoretical natural science in general. These three years account for nearly all of his life spent outside New Haven.

In 1869, he returned to Yale and was appointed Professor of Mathematical Physics in 1871, the first such professorship in the United States and a position he held for the rest of his life. The appointment was unpaid at first, a situation common in Germany and otherwise not unusual at the time, because Gibbs had yet to publish anything. Between 1876 and 1878 Gibbs wrote a series of papers on the graphical analysis of multi-phase chemical systems. These were eventually published together in a monograph titled On the Equilibrium of Heterogeneous Substances, his most renowned work. It is now deemed one of the greatest scientific achievements of the 19th century, and one of the foundations of physical chemistry. In these papers Gibbs applied thermodynamics to interpret physicochemical phenomena, successfully explaining and interrelating what had previously been a mass of isolated facts.

"It is universally recognised that its publication was an event of the first importance in the history of chemistry. ... Nevertheless it was a number of years before its value was generally known, this delay was due largely to the fact that its mathematical form and rigorous deductive processes make it difficult reading for anyone, and especially so for students of experimental chemistry whom it most concerns... " (J J O'Connor and E F Robertson, J. Willard Gibbs)

Some important topics covered in his other papers on heterogeneous equilibria include:

Willard Gibbs’ 1873 available energy (free energy) graph, which shows a plane perpendicular to the axis of v (volume) and passing through point A, which represents the initial state of the body. MN is the section of the surface of dissipated energy. Qε and Qη are sections of the planes η = 0 and ε = 0, and therefore parallel to the axes of ε (internal energy) and η (entropy) respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its available energy (Gibbs free energy) and its capacity for entropy (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume) respectively.

Gibbs also wrote on theoretical thermodynamics. In 1873, he published a paper on the geometric representation of thermodynamic quantities. This paper inspired Maxwell to make (with his own hands) a plaster cast illustrating Gibbs's construct which he then sent to Gibbs. Yale proudly owns it to this day.

Later years

In 1880, the new Johns Hopkins University in Baltimore, Maryland offered Gibbs a position paying $3000. Yale responded by raising his salary to $2000, and he did not leave New Haven. From 1880 to 1884, Gibbs combined the ideas of two mathematicians, the quaternions of William Rowan Hamilton and the exterior algebra of Hermann Grassmann to obtain vector analysis (independently formulated by the British mathematical physicist and engineer Oliver Heaviside). Gibbs designed vector analysis to clarify and advance mathematical physics.

From 1882 to 1889, Gibbs refined his vector analysis, wrote on optics, and developed a new electrical theory of light. He deliberately avoided theorizing about the structure of matter (a wise decision, given the revolutionary developments in subatomic particles and quantum mechanics that began around the time of his death), developing a theory of greater generality than any other theory of matter extant in his day.

After 1889, he worked on statistical mechanics, laying a foundation and "providing a mathematical framework for quantum theory and for Maxwell's theories" [3] He wrote classic textbooks on statistical mechanics, which Yale published in 1902. Gibbs also contributed to crystallography and applied his vector methods to the determination of planetary and comet orbits.

Not much is known about the names and careers of Gibbs's students.

Gibbs never married, living all his life in his childhood home with a sister and his brother-in-law, the Yale librarian. His focus on science was such that he was generally unavailable personally. His protégé E.B. Wilson explains: "Except in the classroom I saw very little of Gibbs. He had a way, toward the end of the afternoon, of taking a stroll about the streets between his study in the old Sloane Laboratory and his home -- a little exercise between work and dinner -- and one might occasionally come across him at that time." Gibbs died in New Haven and is buried in Grove Street Cemetery.

Scientific recognition

Recognition was slow in coming, in part because Gibbs published mainly in the Transactions of the Connecticut Academy of Sciences, a journal edited by his librarian brother-in-law, little read in the USA and even less so in Europe. At first, only a few European theoretical physicists and chemists, such as the Scot James Clerk Maxwell, paid any attention to his work. Only when Gibbs's papers were translated into German (then the leading language for chemistry) by Wilhelm Ostwald in 1892, and into French by Henri Louis le Chatelier in 1899, did his ideas receive wide currency in Europe. His theory of the phase rule was experimentally validated by the works of H. W. Bakhuis Roozeboom, who showed how to apply it in a variety of situations, thereby assuring it of widespread use.

Gibbs was even less appreciated in his native America. Nevertheless, he was recognised as follows:

During his lifetime, American colleges and secondary schools emphasized classics rather than science, and students took little interest in his Yale lectures. (That scientific teaching and research are a fundamental part of the modern university emerged in Germany during the 19th century and only gradually spread from there to the USA.) Gibbs's position at Yale and in American science generally has been described as follows:

"In his later years he was a tall, dignified gentleman, with a healthy stride and ruddy complexion, performing his share of household chores, approachable and kind (if unintelligible) to students. Gibbs was highly esteemed by his friends, but American science was too preoccupied with practical questions to make much use of his profound theoretical work during his lifetime. He lived out his quiet life at Yale, deeply admired by a few able students but making no immediate impress on American science commensurate with his genius." (Crowther 1969: nnn)

This is not to say that Gibbs was unknown in his day. For example, the mathematician Gian-Carlo Rota, while casually browsing the mathematical stacks of Sterling Library, stumbled on a handwritten mailing list attached to some of Gibbs's course notes. It listed over two hundred notable scientists of his day, including Poincaré, Hilbert, Boltzmann, and Mach. One can conclude that Gibbs's work was better known among the scientific elite of his day than published material suggests.

Gibbs' contributions, however, were not fully recognized until some time after the 1923 publication of Gilbert N. Lewis and Merle Randall's Thermodynamics and the Free Energy of Chemical Substances, which introduced Gibbs's methods to chemists worldwide. These methods also became much of the foundation for chemical engineering.

According to the American Mathematical Society, which established the Josiah Willard Gibbs Lectureship in 1923 to increase public awareness of the aspects of mathematics and its applications, Gibbs is one of the greatest scientists America has ever produced.[6]

In 1945, Yale University created the J. Willard Gibbs Professorship in Theoretical Chemistry, held until 1973 by Lars Onsager, who won the 1968 Nobel Prize in chemistry. This appointment was a very fitting one, as Onsager, like Gibbs, was primarily involved in the application of new mathematical ideas to problems in physical chemistry, especially statistical mechanics. Yale's J. W. Gibbs Laboratory and J. Willard Gibbs Assistant Professorship in Mathematics are also named in his honor. On February 28, 2003, Yale held an symposium on the centennial of his death.[7]

Rutgers University has a J. Willard Gibbs Professorship of Thermomechanics presently held by Bernard D. Coleman.[8]

In 1950, Gibbs was elected to the Hall of Fame for Great Americans.

On May 4, 2005, the United States Postal Service issued the American Scientists commemorative postage stamp series, depicting Gibbs, John von Neumann, Barbara McClintock and Richard Feynman.

Nobelists derived from the works of Gibbs

The following individuals won a Nobel Prize in whole or in part by building on Gibbs's work:

  • At the turn of the 20th century, Gilbert N. Lewis and Merle Randall used and extended Gibbs's work on chemical thermodynamic, published their results in the 1923 textbook Thermodynamics and the Free Energy of Chemical Substances, one of the two founding books in chemical thermodynamics. In the 1910s, William Giauque entered the College of Chemistry at Berkeley, where he received a bachelor of science degree in chemistry, with honors, in 1920. At first he wanted to become a chemical engineer, but soon developed an interest in chemical research under Lewis's influence. In 1934, Giauque became a full Professor of Chemistry at Berkeley. In 1949, he won the Nobel Prize in Chemistry for his studies in the properties of matter at temperatures close to absolute zero, studies guided by the third law of thermodynamics.


The greatest thermodynamicist of them all
…who founded a new department of chemical science which is becoming comparable in importance with that created by Lavoisier.
Willard Gibbs is, in my opinion, one of the most original and important creative minds in the field of science America has produced.
To physical chemistry he gave form and content for a hundred years.
Just as Newton first conclusively showed that this is a world of masses, so Willard Gibbs first revealed it as a world of systems.
Gibbs Phase Rule, a general theorem of thermodynamics which is so fundamental that it is unlikely ever to be overthrown
They laugh best who laugh last. Wait till we're dead twenty years. Look at the way they're treating poor Willard Gibbs, who during his lifetime can hardly have been considered any great shakes at New Haven. was not Einstein or Planck or Heisenberg, but Willard Gibbs who brought on the first great revolution in twentieth century physics...
Howard Scott leader of the Technical Alliance and later Technocracy Incorporated cited Gibbs as the intellectual scientific forefather of the concepts of Technocracy.[13][14]


  • "Mathematics is a language." (reportedly spoken by Gibbs at a Yale faculty meeting)
  • "A mathematician may say anything he pleases, but a physicist must be at least partially sane."
  • "It has been said that 'the human mind has never invented a labor-saving machine equal to algebra.' If this be true, it is but natural and proper that an age like our own, characterized by the multiplication of labor-saving machinery, should be distinguished by the unexampled development of this most refined and most beautiful of machines." (1887, quoted in Meinke and Tucker 1992: 190)

See also


  1. Wheeler, Lynde, Phelps (1951). Josiah Willard Gibbs - the History of a Great Mind. Ox Bow Press. ISBN 1-881987-11-6. 
  2. Josiah Willard Gibbs - Britannica 1911
  3. J. J. O'Connor and E. F. Robertson, "J. Willard Gibbs".
  4. Müller, Ingo (2007). A History of Thermodynamics - the Doctrine of Energy and Entropy. Springer. ISBN 978-3-540-46226-2. 
  5. Willard Gibbs Medal - Founded by William A. Converse in 1910
  6. Josiah Willard Gibbs Lectures - American Mathematical Society
  7. J. Willard Gibbs and his Legacy: A Double Centennial - Yale University (2003).
  8. J. Willard Gibbs Professor of Thermomechanics - Rutgers University.
  9. 9.0 9.1 How I Became an Economist by Paul A. Samuelson, 1970 Laureate in Economics, 5 September 2003
  10. Liossatos, Panagis, S. (2004). "Statistical Entropy in General Equilibrium Theory," (pg. 3). Department of Economics, Florida International University.
  11. "Maximum Principles in Analytical Economics", Nobel Prize Lecture
  12. Fenn, John, B. (1982). Engines, Energy, and Entropy – a Thermodynamics Primer. W.H. Freeman and Co. ISBN 0-7167-1281-4. 
  13. History and Purpose of Technocracy by Howard Scott
  14. The Origins of Technocracy. From the Technocracy Movement website - Scott's statement is on the video

Further reading


  • 1947. The Early Work of Willard Gibbs in Applied Mechanics, New York, Henry Schuman
  • 1961. Scientific Papers of J Willard Gibbs, 2 vols. Bumstead, H. A., and Van Name, R. G., eds. ISBN 0918024773
  • Elementary Principles in Statistical Mechanics.

Secondary :

  • Online bibliography.
  • American Institute of Physics, 2003 (1976). Josiah Willard Gibbs
  • Bumstead, H. A., 1903. "Josiah Willard Gibbs" American Journal of Science XVI(4).
  • Crowther, J. G., 1969. Famous American Men of Science. ISBN 0836900405
  • Donnan, F. G., Haas, A. E., and Duhem, P. M. M., 1936. A Commentary on the Scientific Writings of J Willard Gibbs. ISBN 0405125445
  • Hastings, Charles S. ,1909. Josiah Willard Gibbs. Biographical Memoirs of the National Academy of Sciences 6:372–393.
  • Longley, W. R., and R. G. Van Name, eds., 1928. The Collected Works of J Willard Gibbs.
  • Meinke, K., and Tucker, J. V., 1992, "Universal Algebra" in Abramsky, S., Gabbay, D., and Maibaum, T. S. E., eds., Handbook of Logic in Computer Science: Vol. I. Oxford Univ. Press: 189-411. ISBN 0198537611
  • Muriel Rukeyser, 1942. Willard Gibbs: American Genius. Woodbridge, CT: Ox Bow Press. ISBN 0918024579.
  • Seeger, Raymond John, 1974. J. Willard Gibbs, American mathematical physicist par excellence. Pergamon Press. ISBN 0080180132
  • Wheeler, L. P., 1952. Josiah Willard Gibbs, The History of a Great Mind. ISBN 1881987116
  • Edwin Bidwell Wilson (1931) "Reminiscences of Gibbs by a student and colleague", Scientific Monthly 32:211-27.

External links

NAME Gibbs, J. Willard
DATE OF BIRTH February 11, 1839
PLACE OF BIRTH New Haven, Connecticut, U.S.
DATE OF DEATH April 28, 1903
PLACE OF DEATH New Haven, Connecticut, U.S.
ca:Josiah Willard Gibbs

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