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Leonard Euler (1707--1783) --- Historical sketch

It is in tones of awe that mathematicians speak of Euler.

Leonhard Euler was the most prolific writer of mathematics ever. He made major contributions to geometry, calculus, and number theory; and he developed mathematical analysis, building on Leibniz's differential calculus and Newton's method of fluxions. He is credited with introducing the notation $f\left( x\right) $ for a function (1734), establishing the letter $e$ for the base of natural logarithms (1727), the letter $i$ for the square root of $-1$ (1777), the Greek letter $\pi $ for the ratio of the diameter of a circle to its circumference, and the Greek letter $\QTR{bs}{\Sigma }$ for summation (1755).

Euler was born in Basel, Switzerland. His father had been an undergraduate student with Johann Bernoulli at the University of Basel, though his father was studying for the ministry. But his father did attend some mathematics lectures by Jacob Bernoulli, and the young Leonhard benefitted from his father's teaching thereof.

To indulge his father's wishes, Leonhard entered the University of Basel at age 14 to study for the ministry. Professor Johann Bernoulli at Basel was able to see his potential for mathematics and provided him with advice and occasional weekend assistance. Such familial connections also allowed the young Euler to associate with two of Bernoulli's sons, Nicolaus and Daniel, who themselves became mathematicians. At age 16, Euler was awarded a Masters Degree in Philosophy and undertook studies in theology. But with Johann Bernoulli's help, he persuaded his father to let him pursue mathematics instead, obtaining his doctorate under Johann Bernoulli at age 19.

The next year, he arrived in St. Petersburg, Russia, to assume a post in the mathematical-physical division of the St. Petersburg Academy of Sciences, becoming Professor of Physics at age 23, then progressing to become the Academy's chief mathematician three years later. Shortly afterward, he married the daughter of a local painter, who was from a Swiss family. They eventually had 13 children. The St. Petersburg Academy established a research journal which was soon replete with research papers by Euler. It is said that many of those papers were written while he played with his children.

When he was 28, Euler lost the sight in his right eye, but his research output continued unabated. Indeed, the very next year, he summed an infinite series that had dumbfounded his predecessors: the sum of the infinite seriesMATHThe mathematician Henry Oldenburg posed this problem (called the Basel problem) to Gottfried Leibniz in 1673, but evidently Leibniz was unable to answer. Nor was Jacques Bernoulli able to find the sum in 1689. But Euler. in about 1736, showed thatMATHEuler was a genius at both calculations and in noticing connections, among which is the remarkable equationMATHconnecting the transcendental numbers $e$ and $\pi $ with the imaginary unit $i$ and the most basic numbers $0$ and $1.$

In 1741, at age 34, after having won the Grand Prize of the Paris Academy for the second time, Euler was persuaded to join the Berlin Academy of Science where for 25 years he continued his huge production of mathematical research.

In 1766, Euler returned to St. Petersburg and became almost blind through an illness. A fire destroyed his home a few years later, but he was able to save his mathematical papers. He became completely blind shortly after that. But that did not stop him; he produced about half his lifetime production of mathematics while he was blind. He died in 1873 of a brain hemorrhage. After his death, it took the St. Petersburg Academy some 50 years to complete the publication of his works which totaled some 70 volumes.


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Euler's method

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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