# Euler, Leonhard

### academy mathematics history mathematician

[oy ler] (1707–83) Swiss mathematician: the most prolific mathematician in history.

Euler was the son of a Calvinist pastor who gave him much of his early education, including mathematics. Later he studied at the University of Basle, where he became close friends with members of the Bernoulli family, and in particular. Because he was still rather young (he graduated at 16), Euler could not obtain a post at the university. However, Daniel persuaded Euler to join him at Catherine I’s Academy of Science at St Petersburg in 1727. The Empress died the day Euler arrived in Russia and the future of the academy became uncertain. After an unhappy period working in the Naval College and medical section of the Academy he became professor of physics in 1730. When Bernoulli returned to Switzerland in 1733 Euler succeeded him as professor of mathematics.

The repressive reign of a boy Tsar led Euler, now married, to retreat into reclusive mathematical work, and this solitariness increased during the reign of Anna Ivanovna (1730–40) which was one of the bloodiest in Russian history. During this time Euler lost the sight of his right eye, perhaps due to looking at the Sun accidentally during his astronomical studies. Although conditions eased in Russia after Anna’s death, Euler departed to join Frederick the Great’s Berlin Academy of Science in 1741. Despite great authority in mathematics Euler frequently engaged ineptly in philosophical discussions and Frederick sought a replacement. In 1766 Euler took up Catherine the Great’s offer of the directorship of the St Petersburg Academy, accompanied by his family and servants (18 people in all). He became totally blind soon after his arrival, but due to his remarkable ability to calculate in his head his productivity did not diminish and he successfully carried out his work for another 15 years. He remained in Russia for the rest of his life.

Euler was the most prolific mathematician in history and contributed to all areas of pure and applied mathematics. In analysis he lacked rigour but he had a gift for deducing important results by intuition or by new ways of calculating quantities. He systematized much of analysis, cast calculus and trigonometry in its modern form and showed the important role of e (Euler’s number, 2.718 28…). Euler developed the use of series solutions, paying due regard to convergence; he solved linear differential equations and developed partial differential calculus. He applied these analytical tools to great effect in problems in mechanics and celestial mechanics and introduced the principle of virtual work. The formidable three-body problem of the Earth, Sun and Moon system was solved approximately by him (1753, 1772), leading to an award of £300 by the British Government for the resulting improvement in navigational tables. In the course of this he developed much of classical perturbation theory.

He worked on number theory, fluid flow, geometry and acoustics. A large number of theorems are named after this extraordinarily creative and productive man. One of the best-known is Euler’s rule, which shows that for a polyhedron with *v* vertices, *f* faces and *e* edges, then *v* + *f* – *e* = 2.

He was active in mathematics to the moment of his death, on a day spent partly in calculating the laws of ascent of the recently invented hot-air balloons.

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