Euler, Leonhard
Swiss Geometer and Number Theorist 1707–1783
Leonhard Euler is a name well known in many academic fields: philosophy, hydrodynamics, astronomy, optics, and physics. His true fame comes, however, through his prolific work in pure mathematics. He produced more scholarly work in mathematics than have most other mathematicians. His abilities were so great that his contemporaries called him "Analysis Incarnate."
Euler (pronounced "oiler") was born in Switzerland in 1707. He had originally intended to follow the career path of his father, who was a Calvinist clergyman. Euler studied theology and Hebrew at the University of Basel.
Johann Bernoulli, however, tutored Euler in mathematics on the side. Euler's facility in the subject was so great that his father, an amateur mathematician himself, soon favored the decision of his son to pursue mathematics rather than join the clergy.
Euler first taught at the Academy of Sciences in St. Petersburg, Russia, in 1727. He married and eventually became the father of thirteen children. His children provided him with great joy, and children were often playing in the room or sitting on his lap while Euler worked. It was in Russia that he lost sight in one eye after working for three days to solve a mathematics problem that Academy members urgently needed but had predicted would take months to solve.
Euler was a very productive writer, completing five hundred books and papers in his lifetime and having four hundred more published posthumously. The Swiss edition of his complete works is contained in seventy-four volumes. He wrote Introductio in Analysin Infinitorum in 1748. This book introduces much of the material that is found in modern algebra and trigonometry textbooks.
Euler wrote the first treatment of differential calculus in 1755 in Institutiones Calculi Differentialis and in 1770 explored determinate and indeterminate algebra in Anleitung zur Algebra. Three-dimensional surfaces and conic sections were also extensively treated in his writings.
Euler introduced many of the important mathematical symbols that are now in standard usage, such as Σ (for summation), π (the ratio of the circumference of a circle to its diameter), f(x) (function notation), e (the base of a natural logarithm), and i (square root of negative one). He was the first to develop the calculus of variations. One of the more notable equations that he developed was cosθ + isinθ = eiθ, which shows that exponential and trigonometric functions are related. Another important equation he developed establishes a relationship among five of the most significant numbers, eπi + 1 = 0.
All of Euler's work was not strictly academic, however. He enjoyed solving practical problems such as the famous "seven bridges of Königsberg" problem that led to Euler circuits and paths. He even performed calculations simply for their own sake.
Euler later went to Berlin to become the director of Mathematics at the Academy of Science under Frederick the Great and to enjoy a more free political climate. However, Euler was viewed as being rather unsophisticated, and Frederick referred to him as a "mathematical Cyclops." He returned to Russia when a more liberal leader, Catherine the Great, came to rule.
By 1766, Euler was completely blind but continued to dictate his work to his secretary and his children. His last words, uttered as he suffered a fatal stroke in 1783, imitated his work in eloquence and simplicity: "I die."
Bibliography
Ball, W. W. Rouse. A Short Account of the History of Mathematics, 4th ed. New York: Dover Publications, 1960.
Bell, E. T. Men of Mathematics. New York: Simon and Schuster, 1986.
Benson, Donald C. The Moment of Proof: Mathematical Epiphanies. New York: Oxford University Press, 1999.
Hollington, Stuart. Makers of Mathematics. London: Penguin Books, 1994.
Motz, Lloyd, and Jefferson Hane Weaver. The Story of Mathematics. New York: Avon Books, Inc., 1993.
Parkinson, Claire L. Breakthroughs: A Chronology of Great Achievements in Science and Mathematics. Boston: G. K. Hall & Co., 1985.
