**Leonhard Euler, Power Mathematician**

1707 - 1783 AD Switzerland, Germany

"To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages. "

"Madam, I have come from a country where people are hanged if they talk."

### [In Berlin, excusing his taciturnity in conversation with the Queen Mother of Prussia, on his return from Russia]

**1727** St Petersburg; Euler introduces the symbol e for the base of natural logarithms - not published until 1862.**1735** Euler introduces the notation f(x).**1748** Euler publishes Analysis Infinitorum (Analysis of the Infinite) . . defines a function, mathematical analysis is the study of functions. Bases calculus on the theory of elementary functions rather than on geometric curves, as previously. The famous formula ei = -1 appears for the first time.**1751** Euler publishes his theory of logarithms of complex numbers.**1752** Euler states his theorem V - E + F = 2 for polyhedra.**1765** Euler publishes Theory of the Motions of Rigid Bodies - the foundation of analytical mechanics.**1770** Euler publishes his textbook "Algebra."**1777** Euler introduces the symbol i to represent the square root of -1 in a manuscript which is not printed until 1794.

## Biographical Info

http://www-gap.dcs.st-and.ac.uk/~history/Chronology/1720_1740.html#1727

## Activities and Links

A Proof that e is Irrational

http://mathforum.org/isaac/problems/eproof.html

Euler's Seven Bridges of Konigsberg

http://mathforum.org/isaac/problems/bridges1.html

Euler's Formula

http://www.math.wichita.edu/history/topics/geometry.html#euler

Proofs of Euler's Formula

http://www.ics.uci.edu/~eppstein/junkyard/euler/

Platonic Solids and Euler

http://www.georgehart.com/virtual-polyhedra/platonic-info.html