Leonhard Euler (1707-1783) published his first mathematical work in 1726, one year before Isaac Newton's death. Euler's enormous gifts and broad interests were ideally suited to this slot in history. In pure mathematics and mathematical physics, his work elaborated that of his predecessors, such as Newton and Leibniz, and exerted an enormous influence on those who followed him. Euler also systematized, standardized, and generally cleared the way for mathematical applications in numerous fields. In the course of his long and productive career, Euler "worthily united the ages of Newton and Gauss" (Morgan 133).

Euler was the most prolific mathematician in history. During his career, he published around 560 books and articles, and still left a backlog of over 300 works at his death. The St. Petersburg Academy did not finish publishing his "literary output" until 1862 (Youschkevitz 483). Remarkable as it was, the quantity of the work did not exceed its quality. Euler established several new branches of mathematics; "graph theory, the calculus of variations, and combinatorial topology" -- the last of these only becoming a major research area in the late twentieth century (Dunham 52). In addition, Euler made important contributions to applied mathematics in everything from acoustics and optics to ship building and the structures of music -- although his book on music was said to contain "too much geometry for musicians and too much music for geometers" (qtd. in Dunham 52).