Josiah Willard Gibbs was an American engineer, theoretical physicist, and chemist noted for his famed 1876 publication of On the Equilibrium of Heterogeneous Substances, a graphical analysis of multi-phase chemical systems, which laid the basis for a large part of modern-day science. As one of the greatest American scientists, he devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he was an inventor of vector analysis. He spent his entire career at Yale, which awarded him the first American Ph.D. in engineering in 1863. In 1880, for his work in heat, Gibbs was awarded the Rumford Prize by the American Academy of Arts and Sciences.