At the age of 14, Euler entered the University of Basel where its most famous professor, John Bernoulli, aroused his interest in mathematics; he graduated three years later with a master’s degree. Unsuccessful in obtaining a position at Basel (partly due to his youth), Euler went to the fledgling St. Petersburg Academy in Russia, there to become its chief mathematician by 1730. In 1741, at the invitation of Frederick the Great, he joined the Berlin Academy as head of its mathematics section. Euler’s quarter-century stay was not altogether happy and so, in 1766, he readily accepted the generous offer of Catherine I to return to St. Petersburg. Euler had previously lost the sight in one eye, to all appearances from overwork; in 1771, a clumsy cataract operation on his other eye left him entirely blind. Aided by a phenomenal memory Euler remained productive until the end of his life, dictating his thoughts to a servant who knew no mathematics.

Euler’s enormous output of 886 papers and books made him the most prolific of all mathematicians. His landmark textbooks, the Introductio in analysin infinitorum of 1748 followed by the Introductiones calculi differentialis (1775) and the Institutiones calculi integralis (1768-1770), brought together everything that was then known of the calculus. These comprehensive works divorced the subject from its geometrical origins and shaped its direction for the next 50 years. They also popularized the use of the mathematical symbols

At a time when the notion of convergence was not well-understood, Euler’s work was conspicuous for its treatment of infinite series. His most famous result in this regard involves an unexpected appearance of p : namely,

In the Introductio, he expanded the trigonometric functions sin x and cos x as power series to obtain the relationship now known as Euler’s Identity:

A consequence of taking x = p in Euler’s Identity is an equation connecting five of the most important constants in mathematics: e^ip + 1 = 0. Euler’s investigations also led to the well-known formula