Swiss mathematician, the most prolific mathematician in history, whose collected works fill more than seventy volumes. Working chiefly at the Russian and Prussian academies of science, he standardized much of modern mathematical notation (f(x), e, i, the summation sign), founded graph theory by solving the Seven Bridges of Konigsberg problem in 1736, produced the identity e^(i*pi) + 1 = 0 linking five of mathematics' most important constants, and continued highly productive work after going completely blind in his last years, dictating results from memory.
Facts
BirthplaceBasel, Swiss Confederacy 2 Death PlaceSaint Petersburg, Russian Empire 2 Nationality / Culture Defining ContributionFounded graph theory (the Konigsberg bridges problem); standardized much of modern mathematical notation; the identity e^(i pi) + 1 = 0. 2 Notable WorkIntroductio in analysin infinitorum (1748); Solutio problematis ad geometriam situs pertinentis (1736, the Konigsberg bridges paper) 2 Connections
Associated With
Studied the constant systematically, proved it irrational, and gave it the letter e that carries his name.
Source MacTutor History of Mathematics Archive
Functions, Concepts Developed and popularized the general modern notion of a function and its f(x) notation.
Source MacTutor History of Mathematics Archive
Euler received Goldbach's original 1742 letter and restated the conjecture in its now-standard even-number form; Goldbach himself is not yet a live entity on this atlas.
Source MacTutor History of Mathematics Archive
Additional Source Goldbach's Conjecture (Wikipedia)Origins section, Euler's June 30 1742 reply
Founding problem: the Seven Bridges of Konigsberg, 1736.
Source Graph Theory (Wikipedia)
Introduced the letter i as the standard notation, 1777.
Source MacTutor History of Mathematics Archive
Pi, Concepts Popularized the Greek letter symbol for the constant in the 1730s and 1740s, though he did not invent the notation.
Source MacTutor History of Mathematics Archive
Attributed Works
Source Wikipedia: Beta function
Source Euler Tour Technique (Wikipedia)
Source Euler-Maclaurin Formula (Wikipedia)
Source Wikipedia: Euler's totient function
Source Wikipedia: Function (Mathematics)
Source Wikipedia: Function (Mathematics)
Source Hypergeometric Function (Wikipedia)
Source Wikipedia: Imaginary Unit
Source Latin Square (Wikipedia)
Source Wikipedia: Perfect number
Source Riemann Zeta Function (Wikipedia)
In Branch
Source MacTutor History of Mathematics Archive
Source MacTutor History of Mathematics Archive
Source MacTutor History of Mathematics Archive
Namesake Of
Proofs Credited
Source Basel Problem (Wikipedia)
Source Euclid-Euler theorem, Wikipedia
Source Euler Brick (Wikipedia)
Why this is disputed. Euler may never have explicitly written down this exact identity in this form, though it follows directly from his 1748 formula.
Source Euler's Identity (Wikipedia)
Source Euler's quadrilateral theorem (Wikipedia)
Source Euler's rotation theorem (Wikipedia)
Source Handshaking Lemma (Wikipedia)
Source Wolfram MathWorld: Pentagonal Number Theorem
Source Proof that e is irrational, Wikipedia
In the Other Atlases
Nationality
Also in Geography Atlas: the nationality of this subject.
Sources
1. Wikipedia: Leonhard Euler
WikipediaLead section, gender referenceQuote, Lead section, gender reference
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.
2. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and Statistics
Euler's Identity (Wikipedia)
Wikimedia FoundationProofs Credited: Euler's Identity, history and attribution sectionQuote, Proofs Credited: Euler's Identity, history and attribution section
historical records suggest Euler may never have explicitly written down this particular form
Graph Theory (Wikipedia)
WikipediaAssociated With: Graph Theory, History sectionQuote, Associated With: Graph Theory, History section
is regarded as the first paper in the history of graph theory
Goldbach's Conjecture (Wikipedia)
Wikimedia FoundationAssociated With: Goldbach Conjecture, Origins section, Euler's June 30 1742 replyQuote, Associated With: Goldbach Conjecture, Origins section, Euler's June 30 1742 reply
That ... every even integer is a sum of two primes, I regard as a completely certain theorem, although I cannot prove it.
Euler's rotation theorem (Wikipedia)
Proofs Credited: Euler's Rotation Theorem, Lead paragraphQuote, Proofs Credited: Euler's Rotation Theorem, Lead paragraph
who proved it in 1775 by means of spherical geometry
Handshaking Lemma (Wikipedia)
Wikimedia FoundationProofs Credited: Handshaking Lemma, Lead sentence, attributionQuote, Proofs Credited: Handshaking Lemma, Lead sentence, attribution
Both results were proven by Leonhard Euler (1736)
Basel Problem (Wikipedia)
Wikimedia FoundationProofs Credited: Basel Problem, Lead sentence, attributionQuote, Proofs Credited: Basel Problem, Lead sentence, attribution
solved by Leonhard Euler in 1734
Euclid-Euler theorem, Wikipedia
Proofs Credited: Euclid-Euler Theorem, LeadQuote, Proofs Credited: Euclid-Euler Theorem, Lead
The theorem is named after mathematicians Euclid and Leonhard Euler, who respectively proved the "if" and "only if" aspects of the theorem.
Proof that e is irrational, Wikipedia
Proofs Credited: Proof That e Is Irrational, LeadQuote, Proofs Credited: Proof That e Is Irrational, Lead
Euler wrote the first proof of the fact that e is irrational in 1737 (but the text was only published seven years later).
Euler-Maclaurin Formula (Wikipedia)
Attributed Works: Euler-Maclaurin Formula, LeadQuote, Attributed Works: Euler-Maclaurin Formula, Lead
The formula was discovered independently by Leonhard Euler and Colin Maclaurin around 1735.
Riemann Zeta Function (Wikipedia)
Wikimedia FoundationAttributed Works: Riemann Zeta Function, LeadQuote, Attributed Works: Riemann Zeta Function, Lead
Leonhard Euler first introduced and studied the function over the reals in the first half of the eighteenth century.
Wikipedia: Imaginary Unit
Wikimedia FoundationAttributed Works: i (The Imaginary Unit), LeadQuote, Attributed Works: i (The Imaginary Unit), Lead
The i notation was introduced by Leonhard Euler.
Wikipedia: Euler's totient function
Attributed Works: Euler's Totient Function, LeadQuote, Attributed Works: Euler's Totient Function, Lead
Leonhard Euler introduced the function in 1763.
Wikipedia: Perfect number
Attributed Works: Perfect Number, Lead sectionQuote, Attributed Works: Perfect Number, Lead section
Two millennia later, Leonhard Euler proved that all even perfect numbers are of this form.
Wikipedia: Beta function
Attributed Works: Beta Function, Lead sectionQuote, Attributed Works: Beta Function, Lead section
The beta function was studied by Leonhard Euler and Adrien-Marie Legendre
Euler Tour Technique (Wikipedia)
Attributed Works: Euler Tour Technique, Lead sectionQuote, Attributed Works: Euler Tour Technique, Lead section
The Euler tour technique (ETT), named after Leonhard Euler
Euler's quadrilateral theorem (Wikipedia)
Proofs Credited: Euler's Quadrilateral Theorem, Lead sectionQuote, Proofs Credited: Euler's Quadrilateral Theorem, Lead section
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler
Euler Brick (Wikipedia)
Proofs Credited: Euler Brick, Lead sectionQuote, Proofs Credited: Euler Brick, Lead section
an Euler brick, named after Leonhard Euler
Wikipedia: Function (Mathematics)
Wikimedia FoundationAttributed Works: Functions, Lead section
example, it is common to write sin x instead of sin(x). Functional notation was first used by Leonhard Euler in 1734. Some widely used functions are represented by
Attributed Works: Function (Mathematics), Lead section
example, it is common to write sin x instead of sin(x). Functional notation was first used by Leonhard Euler in 1734. Some widely used functions are represented by
View the Source Wolfram MathWorld: Pentagonal Number Theorem
Wolfram MathWorldProofs Credited: Pentagonal Number Theorem, Page textQuote, Proofs Credited: Pentagonal Number Theorem, Page text
This identity was proved by Euler (1783)
Latin Square (Wikipedia)
Attributed Works: Latin Square, LeadQuote, Attributed Works: Latin Square, Lead
Euler began the general theory of Latin squares.
Hypergeometric Function (Wikipedia)
Attributed Works: Hypergeometric Function, LeadQuote, Attributed Works: Hypergeometric Function, Lead
Hypergeometric series were studied by Leonhard Euler, but the first full systematic treatment was given by Carl Friedrich Gauss (1813)
Dissenting Readings (1 dissenting reading)
Proofs Credited: Euler's Identity
Euler's 1748 formula, e raised to the power i theta equals cosine theta plus i sine theta, implies the identity at theta equals pi, but no surviving source shows Euler himself explicitly writing the compact equation e to the i pi plus 1 equals 0. The identity's attribution to Euler by eponym reflects that it follows directly from his formula, not a documented instance of Euler writing this exact equation himself.
A dissenting reading, from a reviewerEuler's Identity (Wikipedia), Wikimedia Foundation
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