Gibbs entered Yale U in 1854 to study mathematics and Latin. He remained at Yale, becoming its first doctorate student in engineering (and the first in the USA) in 1863. During the 1870s Gibbs worked on thermodynamics and in the 1880s on vector analysis. He was elected to membership of the NAS in 1879. In 1897 he was elected FRS and was awarded the Society's Copley Medal in 1901. His Elementary Principles of Statistical Mechanics was published in 1902. A lunar crater is named after him.
http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/gibbs-josiah.pdf Biographical memoir and photograph.