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Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American theoretical physicist, 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. His thesis was entitled: On the Form of the Teeth of Wheels in Spur Gearing. 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 his greatest contribution, that 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."