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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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VI.19 Leonhard Euler

b. Basel, Switzerland, 1707; d. Saint Petersburg, Russia, 1783

Analysis; series; rational mechanics; number theory;

music theory; mathematical astronomy;

calculus of variations; differential equations

Euler was one of the most influential and prolific mathematicians in history. His first publication was a 1726 paper on mechanics, and his last was a collection published in 1862, seventy-nine years after his death. There are over eight hundred papers bearing his name, about three hundred of them appearing posthumously, and more than twenty books. His Opera Omnia fill over eighty volumes.

In number theory, Euler introduced the Euler phi function, (n), to denote the number of positive integers less than n and relatively prime ...

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