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

 * Basel Problem
 * Euler's Criterion
 * Euler's Formula
 * Euler's Identity
 * Euler's Theorem
 * Euler-Maclaurin Summation Formula

Definitions
... and the list goes on.
 * Euler Phi Function
 * Euler's Number
 * Euler-Mascheroni Constant

Books and Papers

 * "Elements of Algebra"
 * "Introductio in analysin infinitorum" (Introduction to Analysis of the Infinite) (1748)
 * "Institutiones calculi differentialis" (1755)
 * "Institutionum calculi integralis" (1768–1770)