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, and continued at Yale, gaining his Ph. D. degree in 1863, the first engineering doctorate granted in the United States. He then tutored in Yale College: two years in Latin and a year in what was then called "natural philosophy."

In 1866 he went to Europe to study, spending one year each at Paris, Berlin, and Heidelberg. These three years were almost the only time he was ever away from the New Haven area.

In 1869 he returned to Yale and, in 1871, he was appointed Professor of Mathematical Physics. This was the first professorship in mathematical physics in the United States. It was unpaid, in part because Gibbs had never published; only when he was offered a $3000 salary in 1880 by the new Johns Hopkins University in Baltimore, Maryland, did Yale respond by offering him $2000, which seemingly was enough to keep him in New Haven. He remained at Yale until his death in 1903.

Gibbs never married, but lived with his sister and brother-in-law. His brother-in-law was librarian at Yale and publisher of the *Transactions of the Connecticut Academy of Sciences,* the journal which published most of Gibbs' work.

Since, in the mid-1800s, American colleges had little interest in the sciences and emphasized classics, Gibbs found little student interest in his lectures. The interest in his work came mainly from other scientists, particularly the Scottish physicist James Clerk Maxwell. Even that recognition was slow in coming, because he published in an obscure journal which was not widely read in Europe, and it was only when Wilhelm Ostwald translated his papers into book form in German (in 1888) and Henri Le Châtelier made a French translation (in 1899), that his ideas received wide currency in Europe.

Gibbs' scientific career was divided into four phases:

- Up until 1879, Gibbs' primary contribution was the development and presentation of his theory of thermodynamics. The principal publication of this phase, "On the Equilibrium of Heterogeneous Substances", appeared in two installments in 1876 and 1878. An earlier paper (1873) on the geometric representation of thermodynamic quantities inspired Maxwell to make (with his own hands) a plaster cast illustrating Gibbs' construct, which he sent to Gibbs and which Yale retains with great pride. The 1876-78 paper on heterogeneous equilibria included, among other things,
- The concept of chemical potential,
- His version of the concept of free energy,
- The idea of the Gibbsian ensemble, the basis for the field of statistical mechanics, and
- His famous
*phase rule.*

- From 1880 to 1884, Gibbs was mainly engaged in combining the ideas of the Irish mathematician William Rowan Hamilton on quaternions and the German Hermann Grassmann's
*Theory of Extension (Ausdehnungslehre)*to produce the new mathematical field of vector analysis, especially designed by Gibbs to suit the purposes of mathematical physics. - From 1882 to 1889, except for completing his vector analysis, Gibbs concentrated on optics, developing a new electrical theory of light. As in the case of thermodynamics, he deliberately avoided speculation on the structure of matter, to develop a theory of more generality than any type of matter composition would imply.
- After 1889, Gibbs published little of importance, devoting his time to producing his textbook on statistical mechanics, which was published by Yale in 1902.

Among the honors given to Gibbs' memory after his death, Yale University created the **J. Willard Gibbs Professorship in Theoretical Chemistry**. Held during most of his career at Yale by eventual Nobel Prize laureate Lars Onsager, it was an extremely appropriate title for Onsager, who was primarily involved, like Gibbs, in the application of new mathematical ideas to problems in physical chemistry, especially statistical mechanics.

See also Gibbs phenomenon.