Leonard Euler

born: April 15, 1707 in Basel
died: Sept 18, 1783 in St. Petersburg

Euler calculated without apparent effort, as men breathe, or eagles sustain themselves in the wind.

Extremely prolific — 886 books and papers, 13 children. “Analysis incarnate.” His name is attached to formulas in every branch of classical mathematics. Made important contributions to several fields of engineering and business. Introduced the notations f(x), e, i, .

Euler’s (pronounced “oiler”) father was a Calvinist minister who had studied mathematics under Jacob Bernoulli. He hoped that his son would also enter the ministry but did teach the young Euler mathematics. When Euler entered the University of Basel, he studied theology and Hebrew and also had a one hour lesson each week with Johannes Bernoulli. He became friends with Daniel and Nicolaus Bernoulli, and received a masters degree when he was 17. Then the Bernoullis had to persuade his father to let him continue mathematics rather than become a minister. At 19, Euler won an honorable mention for his solution to the problem posed by the Paris Academy, and later in life won first prize in this international competition 12 times.

The Bernoullis were instrumental in getting Euler a research appointment to the St. Petersburg Academy, in the medical section, under Catherine I, but she died soon after his arrival. A repressive regime and chaotic conditions followed, and Euler moved into the mathematical section of the Academy where he belonged. Euler wanted to return to a position in western Europe, but the frequent arrival of children held him where he was. It was, however, an extremely productive mathematical period for him — it was a dangerous time to speak or be visible so Euler put his energies into research and developed work habits which he used the rest of his life. Euler also wrote textbooks for Russian schools, supervised the government department of geography, and helped revise the system of weights and measures. He remained in Russia until 1740 when he accepted the invitation of Fredrick the Great to join the Berlin Academy where he spent the next 24 years. Euler was not as sophisticated as many in the court of Fredrick, and these years were not completely pleasant. However, he did live relatively well and owned a house in Berlin as well as a farm. The situation in Russia had improved immensely during this time, and in 1766 Catherine the Great induced him to return to St. Petersburg. She gave him (and his 18 dependents) a furnished house and even provided a cook.

About 1735, Euler lost his sight in one eye, and, shortly after his return to Russia, the sight in his other eye began to deteriorate. Euler had always had an outstanding memory and could do enormous calculations in his head, so he prepared for the coming blindness by learning to write formulas on a slate and to dictate mathematics to a son or secretary. He was blind for the last 17 years of his life, and during that time his mathematical productivity actually increased. It was said that Euler had tremendous powers of concentration and that he was even able to do mathematics “with a baby in his lap while the older children played all around him.”

Euler remained a Christian all of his life and often read to his family from the Bible. One story about his religion during his stay in Russia involved the atheistic philosopher Diderot. Diderot had been invited to the court by Catherine the Great, but then annoyed her by trying to convert everyone to atheism. Catherine asked Euler for help, and he informed Diderot, who was ignorant of mathematics, that he would present in court an algebraic proof of the existence of God, if Diderot wanted to hear it. Diderot was interested, and, according to De Morgan, Euler advanced toward Diderot, and said gravely, and in a tone of perfect conviction: “Sir, ( a + bn )/n = x , hence God exists; reply! ” Diderot had no reply, and the court broke into laughter. Diderot immediately returned to France.

Euler made fundamental contributions to several areas of science including fluid dynamics, lunar orbit theory (tides), mechanics and “the mathematical theory of investment” (insurance, annuities, pensions), as well as to essentially all of the areas of mathematics which existed at that time. He remained active and alert right up to his death from a stroke at the age of 76.

“Euler” functions and formulas are very common in mathematics. Two of the most famous are:

  • eix = cos(x) + i sin(x) (when x = π we get e + 1 = 0 ), and
  • V – E + F = 2 for any simple closed polyhedron with V vertices, E edges and F faces.

Condensed from Men of Mathematics by E.T. Bell (1937, Simon and Schuster), and An Introduction to the History of Mathematics , 4th ed., by Howard Eves (1976, Holt, Rinehart and Winston). DTH

Last Updated September 21, 2022