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Georg Cantor

File:Georg_Cantor_(Porträt).jpg · Wikimedia Commons · See Wikimedia Commons

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Georg Cantor

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Also known as Georg Ferdinand Ludwig Philipp Cantor, Cantor

German mathematician, inventor of set theory (1845–1918)

OverviewAI-generated

Georg Ferdinand Ludwig Cantor was a mathematician, philosopher, and university teacher. He worked in the fields of set theory, mathematics, mathematical logic, and cardinal numbers. His notable works include *Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrische Reihen* and *Zur Theorie der zahlentheoretische Functionen*. He received the Sylvester Medal.

Cantor was born in Saint Petersburg in 1845 and died in Halle (Saale) on January 6, 1918, from a myocardial infarction. He suffered from major depressive disorder. He was educated at Martin Luther University Halle-Wittenberg, Technical University of Darmstadt, and ETH Zurich. His doctoral advisors were Ernst Kummer and Karl Weierstraß. He was employed by Martin Luther University Halle-Wittenberg.

He held citizenship in the German Reich and the German Empire. He was a member of the German Academy of Sciences Leopoldina, the Göttingen Academy of Sciences and Humanities in Lower Saxony, the Royal Society of Edinburgh, and the London Mathematical Society.

Synthesized by Vinony from 37 facts across 7 sources: Wikidata, Crossref, Open Library, MusicBrainz, Last.fm, Wikiquote, Vinony graph. Generated from structured data (not the Wikipedia text) and checked against those facts — may still contain errors.

Person · Open Library

Born
1845
Died
1918
Works
28

Top works

  • Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrische Reihen
  • Zur Theorie der zahlentheoretische Functionen
  • Zum Problem des actualen Unendlichen
  • Über die verschiedenen Standpunkte in bezug auf das Aktualundendliche
  • Ueber einen Satz aus der Theorie der stetigen Mannigfaltigkeiten

via Open Library + Wikidata

Music · MusicBrainz

Type
Person
Gender
Male
Origin
United States
Active from
1892-01-31
Active to
1964-10-10

Discography

Official siteDiscogsStream

via MusicBrainz · CC0

Listeners · Last.fm

Listeners
3
Total plays
5

<a href="https://www.last.fm/music/Georg+Cantor">Read more on Last.fm</a>

via Last.fm · Georg Cantor

Recent publications · Crossref

5 total works indexed

  1. G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences

    · 2007 · cited 54,793x

  2. Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses

    · 2009 · cited 31,498x

  3. Human-level control through deep reinforcement learning

    · 2015 · cited 23,789x

  4. SARS-CoV-2 Cell Entry Depends on ACE2 and TMPRSS2 and Is Blocked by a Clinically Proven Protease Inhibitor

    · 2020 · cited 17,431x

  5. Microstructural development in equiatomic multicomponent alloys

    · 2004 · cited 9,691x

via Crossref · CC0

Quotes

  • “In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi.”
  • “I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.”
  • “Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!”
  • “There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.”
  • “In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand through a definition. However, this domain cannot itself be something variable, since otherwise each fixed support for the study would collapse. Thus this domain is a definite, actually infinite set of values. Hence each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite.”
  • “The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.”

via Wikiquote · CC BY-SA

~40 min read

Encyclopedic overview

Georg Ferdinand Ludwig Philipp Cantor (/ˈkæntɔːr/ KAN-tor; German: [ˈɡeːɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfɪlɪp ˈkantoːɐ̯]; 3 March [O.S. 19 February] 1845 – 6 January 1918) was a mathematician who played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.

Originally, Cantor's theory of transfinite numbers was regarded as counter-intuitive – even shocking. This caused it to encounter resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections; see Controversy over Cantor's theory. Cantor, a devout Lutheran Christian, believed the theory had been communicated to him by God. Some Christian theologians (particularly neo-Scholastics) saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God – on one occasion equating the theory of transfinite numbers with pantheism – a proposition that Cantor vigorously rejected. Not all theologians were against Cantor's theory; prominent neo-scholastic philosopher Konstantin Gutberlet [de; it] was in favor of it, and Cardinal Johann Baptist Franzelin accepted it as a valid theory (after Cantor made some important clarifications).

Excerpted from Wikipedia’s “Georg Cantor” article, available under the CC BY-SA 4.0 licence.

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