Mathematician:Leonhard Paul Euler

Swiss mathematician and physicist who pioneered much of the foundation of modern mathematics.
 * Introduced much of the notation which is used today, including e and the modern notation for trigonometric functions.
 * Proved Fermat's Little Theorem.
 * In 1783, on the basis of considerable numerical evidence, conjectured the Law of Quadratic Reciprocity, which was eventually proven by Gauss in 1798.


 * Proved the converse of the result known to Euclid, that if $$2^p - 1$$ is prime, then $$2^{p-1} \left({2^p - 1}\right)$$ is perfect. That is, Euler proved that if $$n$$ is an even perfect number, then $$n$$ is of the form $$2^{p-1} \left({2^p - 1}\right)$$ where $$p$$ is prime. The results together are known as the Theorem of Even Perfect Numbers.

Nationality
Swiss

History

 * Born: 15 April 1707
 * Died: 18 September 1783

Theorems and Problems

 * Basel Problem
 * Euler's Criterion
 * Euler's Formula
 * Euler's Identity
 * Euler Polyhedron Formula
 * Euler's Theorem
 * Euler-Maclaurin Summation Formula
 * Theorem of Even Perfect Numbers
 * The Bridges of Königsberg Problem

Definitions
... and the list goes on.
 * Euler Characteristic
 * Euler Phi Function
 * Euler's Number
 * Euler-Mascheroni Constant
 * Eulerian Circuit
 * Eulerian Graph
 * Semi-Eulerian Graph
 * Eulerian Path

Books and Papers

 * 1736-37: Mechanica
 * 1739: Tentamen Novae Theoriae Musicae
 * 1740: Methodus Inveniendi Lineas Curvas
 * 1748: Introductio in Analysin Infinitorum
 * 1755: Institutiones Calculi Differentialis
 * 1765: Theoria Motus Corporum Solidorum
 * 1768-70: Institutionum Calculi Integralis