# Leonhard Euler

# Leonhard Euler

**1707-1783**

**Swiss Mathematician**

The mathematician Leonhard Euler (pronounced "oiler") was one of the great geniuses of his age, a thinker who explored virtually every known area of his chosen field. Nearly 900 books and papers are attributed to him, many of them written in the last 17 years of his life, when he was completely blind. (Euler had been blind in one eye for the preceding 31 years.) His interests ranged from analytic geometry to differential and integral calculus to the calculus of variations. Like many mathematicians of his day, his work also involved questions of applied mathematics: on the day he died, Euler had just finished calculating the orbit of the recently discovered planet Uranus.

Born in Basel, Switzerland, on April 17, 1707, the future mathematician was the son of Paul, a Calvinist pastor, and Marguerite Brucker Euler. Soon after his birth, the family moved to the town of Reichen, where his father had a parish. Paul wanted his son to follow him in the ministry; but the gifted boy's tutors, the brothers Jakob (1654-1705) and Johann (1667-1748) Bernoulli, convinced him that God had called Leonhard to a different path, as evidenced by his demonstrated abilities.

As promising as his talents seemed, Euler's first attempts to make a name for himself met with little success. Because he came from land-locked Switzerland and had never seen a ship, he failed to win a contest regarding the optimum placement of masts on sailing ships, sponsored by the Académie Royale des Sciences in France. In time he would win a dozen awards from the distinguished institution; meanwhile, he had difficulty just getting a job. Rejected by the University of Basel, where he hoped to obtain a professorship, he jumped at an offer from Johann's son Daniel Bernoulli (1700-1782) to help him obtain a position teaching medicine at the St. Petersburg Academy in Russia.

By 1733, six years after Euler arrived in St. Petersburg, Bernoulli had returned to Switzerland, and Euler took his place as director of the mathematics department at St. Petersburg. Also in 1733, Euler married Catharina Gsell, the daughter of a Swiss painter who served in the court of Peter the Great. Eventually the couple had 13 children, of whom three sons and two daughters survived. In 1735, Euler lost the sight in his right eye, probably while studying the Sun to solve a problem put forth by the French Académie.

In the 1730s, Euler distinguished himself by solving a number of practical problems on matters such as weights and measures for the Russian government. Less practical, but perhaps more noteworthy, was his solution to the famous Königsberg Bridge Problem. The puzzle involved an attempt to cross seven bridges without backtracking, and Euler's solution helped spawn the field of graph theory. Also during this period, Euler wrote one of his most important works, *Mechanica* (1736-37), in which he became the first to apply mathematical analyses to the laws of dynamics discovered by Sir Isaac Newton (1642-1727).

Dissatisfied with the ever-present state of political oppression in Russia, Euler in 1740 accepted an appointment by Frederick the Great of Prussia to the Berlin Academy. He would remain in the service of the German king for nearly a quarter-century, again assisting with practical matters such as pension plans and the water supply system. It was during this time that Euler produced his famous proof of Pierre de Fermat's (1601-1665) Last Theorem. Though in fact his proof contained an error, Euler's work on the problem helped make possible the development of a successful proof some 250 years later. Also while in Berlin, Euler wrote a number of significant works, of which perhaps the greatest was *Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes* (1744). This book on the calculus of variations led to his election as a Fellow of the Royal Society of London.

Euler had maintained good relations with his former Russian hosts throughout his time in Germany, making it easy to return to Russia in
1766, after a falling-out with Frederick. Catherine the Great, now the czarina, presented Euler with an estate and servants; and during this last phase of his life, the mathematician produced some of his greatest work, including *Institutiones calculi integralis* (1768-70), a classic on integral calculus. This was particularly impressive in light of the fact that he had lost the vision in his left eye to a cataract, and was thus completely blind.

More tragedy followed in 1776, when his wife Catharina died; but in the following year Euler married her aunt and half-sister, Salome Gsell. He continued to work on a number of problems related to astronomy, including questions involving moon phases, right up to the time of his death. Immensely fond of children, Euler died of a stroke while playing with his grandson on September 18, 1783.

**JUDSON KNIGHT**

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**Leonhard Euler**