Interactive Real Analysis
- part of 9.9. Euler, Leonard (1707-1783)
Leonhard Euler was one of top mathematicians of the eighteenth century and the greatest mathematician
to come out of Switzerland. He made numerous contributions to almost every mathematics field and was
the most prolific mathematics writer of all time. It was said that "Euler calculated without apparent effort,
as men breathe...." He was dubbed "Analysis Incarnate" by his peers for his incredible ability.Leonhard Euler was born in Basel, Switzerland, on April 15, 1707. His father, a Calvinist pastor and former mathematician, planned the life of a clergyman for his son and originally Leonhard followed that path. He graduated from the University of Basel in 1724 where he studied theology and Hebrew. During his time at the school, however, he was privately tutored in mathematics by Johann Bernoulli. Johann was so impressed by his pupil's ability that he convinced Euler's father to allow Leonhard to become a mathematician.
Euler took up a position at the Academy of Sciences in St. Petersburg, Russia, in 1727 and became the professor of mathematics six years later. During his stay, he was married and would over his lifetime have thirteen children, five of which would survive to adulthood. While in Russia, he lost sight in one eye after working day and night for three days to solve a problem. The question, which was a public contest, took all the other mathematicians involved months to figure out. He also discovered that the Czar's government was far from democratic as he was followed by secret police. He looked for a way out.
He found it in 1741, when he moved his family to Berlin to take over as director of mathematics at the Academy of Sciences under Frederick the Great. While in Prussia, his home was destroyed by invading Russian armies, but he was held in such high esteem by both countries that he was compensated for more than he lost. He also frustrated Frederick's mother to no end by refusing to engage in conversation. When she finally asked him for a reason, he responded: "Madam, it is because I have just come from a country where every person who speaks in hanged." He also could not handle the intrigues and feuds that plagued the Academy. When the previous president died, Euler should have been the obvious successor except for the fact that Frederick disliked him. The monarch asked D'Alembert, a French mathematician, to take the position. D'Alembert, who saw the injustice, refused on the basis that no one could be placed above Euler. However, it became clear it was time for Leonhard to find a new home.
Meanwhile, Russia had come under the rule of the more liberal Catherine the Great. In 1766, he returned to St. Petersburg and became the director of the Academy. Soon afterwards, he went completely blind but continued his mathematical work by dictating to a secretary. His house burned down in 1771 and his life was saved only by the heroic efforts of a servant to carry him out of the flames. He died of a stroke on September 7, 1783. Appropriately to this simple mathematician, his final words were simply "I die."
Euler was especially famous from his writings. Simply put, he produced more scholarly work on mathematics than anyone. It was said that he could produce an entire new mathematical paper in about thirty minutes and had huge piles of his works lying on his desk. Even more impressive, Euler contemplated new problems not in quiet privacy but in the presence of his young children. It was not uncommon to find "Analysis Incarnate" ruminating over a new subject with a child on his lap.
Though Euler is best remembered for his contributions to mathematics, he was involved in some extent in
almost all fields. Especially close to his heart was philosophy. While in Berlin, he would constantly get
involved in philosophical debates, especially with Voltaire. Unfortunately, Euler's philosophical ability
was limited and he often blundered to the amusement of all involved. However, when he returned to
Russia, he got his revenge. Catherine the Great had invited to her court the famous French philosopher
Diderot, who to the chagrin of the czarina, attempted to convert her subjects to atheism. She asked Euler
to quiet him. One day in the court, the French philosopher, who had no mathematical knowledge, was
informed that someone had a mathematical proof of the existence of God. He asked to hear it. Euler then
stepped forward and stated: "Sir,
,hence God exists; reply!"
Diderot had no idea what Euler was talking about. However, he did understand the chorus of
laughter that followed and soon after returned to France.
Euler's contributions to every mathematical field that existed at the time. He standardized modern
mathematics notation when he used symbols such as f(x), e, 
, i and 
in his textbooks. He was
the first person to represent trigonometric values as ratios and prove that e is an irrational
number. His invention of the calculus of variations led to the general method to solve max and min value
problems. In physics, he developed the general equations for hydrodynamics and for motion. He was also
one of the first people to recognize that infinite series had to be convergent to be used safely. Possibly his
most impressive work was his approximation of the three-body problem of the sun, earth and moon, which
he solved while completely blind and performing all the computations in his head. Among his other
endeavors were proofs of Fermat's final theorem for cubes and quads, the use of calculus in mechanics and
the computation of logs for negative and imaginary numbers.
For related information on Euler, see: Johann Bernoulli , e (Euler's numbers), Euler's sequence, Euler's series.
. Sources
- Alton, Eric J. "Euler." Encyclopedia of World Biography. New York: McGraw-Hill, Inc., 1973. vol. 4, pp. 30-31.
- Bell, E.T. Men of Mathematics. New York: Simon and Schuster, Inc., 1937.
- Muir, Jane. Of Men and Numbers. New York: Dodd, Mead & Company, 1962.
- Turnbull, Herbert Westren. The Great Mathematicians. New York: New York University Press, 1961.