- Wikipedia

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\"Euler\" redirects here. For other uses, see Euler (disambiguation).

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Leonhard Euler
Portrait by Jakob Emanuel Handmann, 1753
Born	(1707-04-15)15 April 1707 Basel, Swiss Confederacy
Died	18 September 1783(1783-09-18) (aged 76) [OS: 7 September 1783] Saint Petersburg, Russian Empire
Education	University of Basel (MPhil)
Known for	Contributions namesakes
Spouses	\n \n Katharina Gsell \n (m. 1734; died 1773) \n \n Salome Abigail Gsell \n (m. 1776) \n
Children	13, including Johann
Awards	FRS (1747)
Scientific career
Fields	Mathematics Physics
Institutions	Imperial Russian Academy of Sciences Berlin Academy
Thesis	Dissertatio physica de sono (Physical dissertation on sound) (1726)
Doctoral advisor	Johann Bernoulli
Doctoral students	Johann Hennert
Other notable students	Nicolas Fuss Stepan Rumovsky Joseph-Louis Lagrange (epistolary correspondent)^[a] Anders Johan Lexell
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Signature

Leonhard Euler (/\u02c8\u0254\u026al\u0259r/ OY-l\u0259r;^[b] German: [\u02c8le\u02d0\u0254nha\u0281t \u02c8\u0294\u0254\u028fl\u0250] ^\u24d8, Swiss Standard German: [\u02c8le\u0254nhard \u02c8\u0254\u028fl\u0259r]; 15 April 1707 – 18 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical terminology and notation, including the notion of a mathematical function.^[6] He is known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.^[7] Euler has been called a \"universal genius\" who \"was fully equipped with almost unlimited powers of imagination, intellectual gifts and extraordinary memory\".^[8] He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia.\n

Euler is credited for popularizing the Greek letter ${\\displaystyle \\pi }$ (lowercase pi) to denote the ratio of a circle's circumference to its diameter, as well as first using the notation ${\\displaystyle f(x)}$ for the value of a function, the letter ${\\displaystyle i}$ to express the imaginary unit ${\\displaystyle {\\sqrt {-1}}}$ , the Greek letter ${\\displaystyle \\Sigma }$ (capital sigma) to express summations, the Greek letter ${\\displaystyle \\Delta }$ (capital delta) for finite differences, and lowercase letters to represent the sides of a triangle while representing the angles as capital letters.^[9] He gave the current definition of the constant ${\\displaystyle e}$ , the base of the natural logarithm, now known as Euler's number.^[10] Euler made contributions to applied mathematics and engineering, such as his study of ships which helped navigation, his three volumes on optics contributed to the design of microscopes and telescopes, and he studied the bending of beams and the critical load of columns.^[11]\n

Euler is credited with being the first to develop graph theory (partly as a solution for the problem of the Seven Bridges of K\u00f6nigsberg, which is also considered the first practical application of topology). He also became famous for, among many other accomplishments, solving several unsolved problems in number theory and analysis, including the famous Basel problem. Euler has also been credited for discovering that the sum of the numbers of vertices and faces minus the number of edges of a polyhedron equals 2, a number now commonly known as the Euler characteristic. In physics, Euler reformulated Isaac Newton's laws of motion into new laws in his two-volume work Mechanica to better explain the motion of rigid bodies. He contributed to the study of elastic deformations of solid objects. Euler formulated the partial differential equations for the motion of inviscid fluid,^[11] and laid the mathematical foundations of potential theory.^[8]\n

Euler is regarded as arguably the most prolific contributor in the history of mathematics and science, and the greatest mathematician of the 18th century.^[12]^[11] His 866 publications and his correspondence are being collected in the Opera Omnia Leonhard Euler which, when completed, will consist of 81 quartos.^[13]^[14]^[15] Several great mathematicians who worked after Euler's death have recognised his importance in the field: Pierre-Simon Laplace said, \"Read Euler, read Euler, he is the master of us all\";^[16]^[c] 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.\"^[17]^[d]\n

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mathematical constant $e$
Part of a series of articles on the

\nProperties
\n Natural logarithm \n Exponential function
\nApplications
\n compound interest \n Euler's identity \n Euler's formula \n half-lives\n exponential growth and decay
\nDefining $e$
\n proof that $e$ is irrational \n representations of $e$ \n Lindemann\u2013Weierstrass theorem
\nPeople
\n John Napier \n Leonhard Euler
\nRelated topics
\n Schanuel's conjecture
v t e

Early life

Career

Saint Petersburg

Berlin

Return to Russia

Personal life

Eyesight deterioration

Death

Contributions to mathematics and physics

Mathematical notation

Analysis

Number theory

Graph theory

Physics, astronomy, and engineering

Logic

Music

Personal philosophy and religious beliefs

Legacy

Recognition

Commemorations

Selected bibliography

Notes

References

Sources

Further reading

External links

Leonhard Euler

Talks

7 January, 1734