# Euler, Leonhard

**Euler, Leonhard** (1707-83): Swiss, Mathematician

Euler was one of the most prolific mathematicians in history and contributed substantially to almost every branch of mathematics. He was born in Basel, Switzerland on 15 April, 1707. His father was a Calvinist minister who determined that his son should also study theology. Euler, however, exhibited impressive talent for mathematics at a young age, and received tutoring from the prominent mathematicians Jakob Burckhardt and Johnann I Bernoulli. Members of the Bernoulli family eventually persuaded Euler’s father to allow him the freedom to pursue the study of mathematics.

After graduating from the University of Basel in 1724, Euler received an invitation from Catharine I to join the Academy of Sciences at St. Petersburg in 1727. There he became professor of physics in 1730, and professor of mathematics in 1733. During these years, Euler produced papers on a wide array of subjects, including navigation, ballistics, mechanics, and measurement, in addition to papers on mathematics. In 1741 he was summoned to Berlin by Frederick II, the Great. There he served as director of mathematics until 1766. In the meantime, he tutored the family of Frederick the Great and solved problems involving mathematics, physics and astronomy for the emperor. Euler’s working relationship with this monarch was problematic, however, and eventually compelled him to return to St. Petersburg in 1766, at the invitation of Catherine II, the Great.

Much of Euler’s legacy to the fields of mathematics and physics can be found in his textbooks. His first textbook, *Introductio in analysin infinitorium* (1748), was published in two volumes. The first volume focuses primarily on exponential, logarithmic, and trigonometric functions. Therein he resolved the problem of logarithms of negative and imaginary numbers. The second volume of this work contains an analytical study of curves and surfaces and is credited as the first treatise on analytical geometry. He also composed the textbook* Vollständige Anleitung zur Algebra* (Thorough Introduction to Algebra, 1770), which also covers the theory of numbers. Most notably, Euler made a lasting contribution to mathematics with his development of function theory and notation.

Euler also dedicated much of his talent to solving problems of physics and astronomy. In his *Mechanica* (1736), Euler presents solutions to problems of hydrodynamics. He even attempted to popularize the disciplines of philosophy and natural science in his three-volume work, *Lettres á une Princesse d’Allemagne*.

The intensity of some of Euler’s pursuits eventually led to his complete blindness. He nevertheless continued to dictate his discoveries in St. Petersburg until his death on September 7, 1783. Works completed in the latter years included a monograph on integral calculus and studies on the topic of fluid mechanics. Euler also earned a prize for his work on astronomy.

The papers that Euler himself had prepared for publication during his lifetime were republished in three series, beginning in 1911, in Leipzig Germany: *Opera mathematica, Opera mechanica et astronomica, and Opera physica*. Scholars have estimated that if the entirety of this prolific mathematician’s works were to be published, they would comprise fifty volumes.

Further Reading:

Celeste Williams Brockington, “Leonhard Euler,” *Great Lives from History*, Vol. 3, 1989.

**Sarah Tusa**

Lamar University