**J**osiah Willard Gibbs (February 11, 1839 – April 28, 1903) 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.

**Biography**

**Early years**

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.

**Middle years**

Gibbs continued his studies at Yale, gaining his Ph. D. degree in 1863. This was 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 Havenarea.

In 1869 he returned to Yale and, in 1871, he was appointed Professor ofMathematical Physics. This was the first professorship in mathematical physics in the United States. It was unpaid, in part because Gibbs had never published.

Gibbs then started work on the development and presentation of his theory of thermodynamics. In 1873, Gibbs 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’ construct (which he sent to Gibbs and which Yale still retains with great pride).

Gibbs next published the paper “On the Equilibrium of Heterogeneous Substances”. This appeared in two installments in 1876 and 1878. Gibbs’ papers on heterogeneous equilibria included:

Some chemical potential concepts

Some free energy concepts

A Gibbsian ensemble ideal (basis of the statistical mechanics field)

A phase rule

**Later years**

In 1880, Gibbs was offered a $3000 salary by the new Johns HopkinsUniversity in Baltimore, Maryland and Yale responded by offering him $2000, which seemingly was enough to keep him in New Haven.

From 1880 to 1884, Gibbs combined the ideas of the Irish mathematician William Rowan Hamilton on quaternions and the German Hermann Grassmann’s Theory of Extension (Ausdehnungslehre) to produce the mathematical field of vector analysis (co-independent formulation; Oliver Heaviside also developed this field). Gibbs designed this to suit the purposes of mathematical physics.

From 1882 to 1889, Gibbs researched optics, developing a new electrical theory of light. Gibbs also completed his vector analysis during this time. Gibbs deliberately avoided theorizing on the structure of matter, developing a theory of more generality than any type of matter composition would imply. After 1889, Gibbs produced textbooks on statistical mechanics, which was published by Yale in 1902.

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.

**Death and afterwards**

Gibbs remained at Yale until his death in 1903.

Since Gibbs died shortly after the inauguration of the Nobel Prizes, he never won a Nobel. However, his receipt of the Copley Medal of the Royal Society of the United Kingdom is regarded as the highest honor available at the time from the international scientific community.

Scientific recognition

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.

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 Chatelier made a French translation (in 1899), that his ideas received wide currency in Europe.