A Swiss mathematician who spent most of his life in Russia, Leonhard Euler is considered the preeminent mathematician of his generation.
Euler was the first to introduce the concept of the function which in and of itself is an immense achievement. That set the stage for all mathematical development since. He was the first to ascribe the letter "e" to mean the base of the natural logarithm, the first to use "i" for the imaginary unit, and he assigned sigma for summation. He introduced Euler's formula, a trigonometric equation, and he developed the Euler's identity, eπi + 1 = 0. His impact on mathematics is profound.
Gauss is considered to be one of history's most influential mathematicians. A German child prodigy, Gauss would later lend his name to an immense amount of discoveries even after his death.
The bell-curved normal distribution is a now central element of modern-day statistics and is sometimes referred to as the Gaussian distribution. Gauss also was interested in the field of differential equations, which are pervasive in modern engineering. He was also central in developing the theorem which established important properties of curvature. He would later co-design the first electromagnetic telegraph in 1833.
Reference:
http://www.businessinsider.com/important-mathematicians-modern-world-2012-7?IR=T#carl-freidrich-gauss-behind-everything-we-know-about-statistics-17
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