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
In Branch
Source MacTutor History of Mathematics Archive
Source MacTutor History of Mathematics Archive
Source MacTutor History of Mathematics Archive
Namesake Of
Derived from the object's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the object's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the object's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the object's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Proofs Credited
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)
In the Other Atlases
- Also in Geography Atlas: Switzerland, nationality there.
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.
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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