Excerpt:
Leonhard Euler is considered by many to be the most prolific mathematician in history. He published 866 books and papers and won the Paris Academy Prize 12 times. He was born in Basel, Switzerland on April 15, 1707 and died on September 18, 1783. Euler was the son of a Lutheran minister and entered the University of Basel to study theology like his father but opted to change his major to mathematics under the advice of Johann Bernoulli. He worked at the St. Petersburg Academy of Science and later at the Berlin Academy of Science. In 1735, Euler lost sight in one eye, and in the late 1760's, he became completely blind. Although blind, Euler had such an incredible memory and mathematical mind, he was able to dictate treatises on algebra, optics, and lunar motion until his death. Francois Arago said of his mathematical talents, "He calculated just as men breathe, as eagles sustain themselves in the air." Once, Euler settled an argument between students whose calculation differed by a digit at the fifteenth decimal place by calculating the answer in his head. Euler's contributions to mathematics include the introduction of the symbols e, i, f(x), , and sigma for summations. He also made significant contributions to differential calculus, mathematical analysis, and number theory, as well as optics, mechanics, electricity, and magnetism.
Euler developed the function, which is defined as the number of positive integers not exceeding m that are relatively prime to m. For example, would equal:
> with(numtheory);
> phi(7);