Josiah Willard Gibbs was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous inductive science. He also worked on the application of Maxwell’s equations to problems in physical optics. As a mathematician, he invented modern vector calculus. In 1863, Yale awarded Gibbs the first American doctorate in engineering.
About Josiah Willard Gibbs in brief

Willard. Gibbs was educated at the Hopkins School and entered Yale College in 1854 at the age of 15. At Yale, he received prizes for excellence in mathematics and Latin, and he graduated in 1858, near the top of his class. At age 19, soon after his graduation from college, Gibbs was inducted into the Connecticut Academy of Arts and Sciences, a scholarly institution composed primarily of members of the Yale faculty. After the death of his father in 1861, Gibbs inherited enough money to make him financially independent. He remained at Yale for the duration of the war and he was not conscripted to fight in the Civil War of 1861–65. The elder Gibbs was generally known to his family and colleagues as “Jos Isaiah” while the son was called “Willard””. The son was a linguist and theologian and served as professor of sacred literature at Yale Divinity School from 1824 until his death in 1861. He later became a professor of mathematical physics at Yale, where he was a Professor of Physics and Astronomy from 1871 to his death. He worked in relative isolation and became the earliest theoretical scientist in the U.S. to earn an international reputation and was praised for his work on thermodynamics. Though his work was almost entirely theoretical, the practical value of Gibbs’s contributions became evident with the development of industrial chemistry during the first half of the 20th century. He used geometrical techniques to investigate the optimum design of gears in which he used in Gearing Spur.
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