German mathematician who created set theory and proved, against the intuitions of most of his contemporaries, that infinite sets come in different sizes: the real numbers are strictly more numerous than the natural numbers, shown by his 1891 diagonal argument. He introduced the notion of cardinality (aleph numbers) to measure the sizes of infinite sets and proposed the continuum hypothesis about the possible sizes between them. His work was fiercely opposed by influential contemporaries, notably Leopold Kronecker, and he suffered repeated episodes of severe depression later in life, dying in a sanatorium in Halle.
Facts
BirthplaceSaint Petersburg, Russian Empire 2 Death PlaceHalle, German Empire, in a sanatorium 2 Nationality / Culture Defining ContributionCreated set theory and proved that infinite sets have different sizes (the diagonal argument), overturning the assumption that all infinities are the same infinity. 3 Notable WorkUeber eine elementare Frage der Mannigfaltigkeitslehre (1891, the diagonal argument paper) 3 Georg Cantor
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Georg Cantor introduced the set in 1883 as an example within his work on point-set topology and the theory of trigonometric series.
Source Cantor Set (Wikipedia)
Source Wikipedia: Cantor's Diagonal Argument
Infinity, Concepts Founded the rigorous mathematical treatment of completed infinities and their differing sizes, from 1874.
Source The Stanford Encyclopedia of Philosophy
Weierstrass was Cantor's teacher in Berlin; no dedicated advisor/student relation type exists on this atlas at claim time (checked dbo.vRelationType), so this is recorded as a general association rather than an invented vocabulary item.
Source Karl Weierstrass, Biography (MacTutor History of Mathematics)
Founder of set theory, 1870s.
Source Set Theory (Wikipedia)
Sets, Concepts Created set theory from 1874 onward.
Source The Stanford Encyclopedia of Philosophy
Conjectures Posed
Source Continuum Hypothesis (Wikipedia)
In Branch
Source The Stanford Encyclopedia of Philosophy
Source The Stanford Encyclopedia of Philosophy
Namesake Of
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)
Proofs Credited
Source Cantor's Theorem (Wikipedia)
In the Other Atlases
- Also in Geography Atlas: Germany, nationality there.
Sources
1. Wikipedia: Georg Cantor
WikipediaLead section, gender referenceQuote, Lead section, gender reference
He defined the cardinal and ordinal numbers and their arithmetic.
2. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and Statistics
3. The Stanford Encyclopedia of Philosophy
Center for the Study of Language and Information, Stanford University
Cantor's Theorem (Wikipedia)
Wikimedia FoundationProofs Credited: Cantor's Theorem, proof and attribution sectionQuote, Proofs Credited: Cantor's Theorem, proof and attribution section
the diagonal argument for the uncountability of the reals also first appears
Continuum Hypothesis (Wikipedia)
Wikimedia FoundationConjectures Posed: Continuum Hypothesis, History sectionQuote, Conjectures Posed: Continuum Hypothesis, History section
The continuum hypothesis was first introduced by Georg Cantor in his 1878 paper
Wikipedia: Cantor's Diagonal Argument
Wikimedia FoundationAssociated With: Cantor's Diagonal Argument, lead paragraph, publication dateQuote, Associated With: Cantor's Diagonal Argument, lead paragraph, publication date
Georg Cantor published this proof in 1891
Set Theory (Wikipedia)
WikipediaAssociated With: Set Theory, Origins sectionQuote, Associated With: Set Theory, Origins section
Cantor is commonly considered the founder of set theory
Karl Weierstrass, Biography (MacTutor History of Mathematics)
MacTutor History of Mathematics Archive, University of St AndrewsAssociated With: Karl Weierstrass, Students sectionQuote, Associated With: Karl Weierstrass, Students section
In 1870 Sofia Kovalevskaya came to Berlin and Weierstrass taught her privately since she was not allowed admission to the university.
Cantor Set (Wikipedia)
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