## Leonhard Euler

**Leonhard Euler**( , is considered incorrect}} ;: .}} 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory.

Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century. Several great mathematicians who produced their work after Euler's death have recognised his importance in the field as shown by quotes attributed to many of them: Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all." Carl Friedrich Gauss wrote: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it." ''"Die besondere Herausgabe der kleinern Eulerschen Abhandlungen ist gewiÃŸ etwas hÃ¶chst verdienstliches, [...] und das Studium aller Eulerschen Arbeiten doch stets die beste durch nichts anderes zu ersetzende Schule fÃ¼r die verschiedenen mathematischen Gebiete bleiben wird."'' [The special publication of the smaller Euler treatises is certainly something highly deserving, [...] and the study of all Euler's works will always remain the best school for the various mathematical fields, which cannot be replaced by anything else.]}} Euler is also widely considered to be the most prolific; his 866 publications as well as his correspondences are collected in the ''Opera Omnia Leonhard Euler'' which, when completed, will consist of 81 ''quarto'' volumes. He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia.

Euler is credited for popularizing the Greek letter $\backslash pi$ (lowercase pi) to denote the ratio of a circle's circumference to its diameter, as well as first using the notation $f(x)$ for the value of a function, the letter $i$ to express the imaginary unit $\backslash sqrt\{-1\}$, the Greek letter $\backslash Sigma$ (capital sigma) to express summations, the Greek letter $\backslash Delta$ (uppercase delta) for finite differences, and lowercase letters to represent the sides of a triangle while representing the angles as capital letters. He gave the current definition of the constant $e$, the base of the natural logarithm, now known as Euler's number.

Euler was also the first practitioner of graph theory (partly as a solution for the problem of the Seven Bridges of KÃ¶nigsberg). He became famous for, among many other accomplishments, solving the Basel problem, after proving that the sum of the infinite series of squared integer reciprocals equaled exactly /6}}, and for discovering that the sum of the numbers of vertices and faces minus edges of a polyhedron equals 2, a number now commonly known as the Euler characteristic. In the field of physics, Euler reformulated Newton's laws of physics into new laws in his two-volume work ''Mechanica'' to better explain the motion of rigid bodies. He also made substantial contributions to the study of elastic deformations of solid objects. Provided by Wikipedia

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