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The Controversial Legacy of Georg Cantor: A Mathematical Genius or Troubled Innovator?

Explore the tumultuous life and groundbreaking contributions of mathematician Georg Cantor, who revolutionized set theory and transfinite numbers but faced criticism and controversy. Delve into his biography, theories, and the ongoing debate surrounding his work.

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The Controversial Legacy of Georg Cantor: A Mathematical Genius or Troubled Innovator?

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  1. Georg Cantor Emre Alpagut CMPE.220 / Dr. Haluk Bingöl 15/11/2016 1

  2. “In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi.” 2

  3. Cantor: A controversial figure “scientific charlatan, renegade, acorrupter of youth” - Leopold Kronecker “one of the greatest intellects of the nineteenth century” - Bertand Russell “Cantor has created a new paradise for mathematicians” - David Hilbert “Cantor's transfinite number represents a grave mathematical malady, a perserve pathological illness that will one day be cured” - Henri Poincare 3

  4. Cantor's Biography: An even more controversial topic • E.T. Bell's Men of Mathematics (1937) • Lack of access to unpublished documents • Adolf Fraenkel's obituary (1930) • Probleme des Unendlichen: Werk und Leben Georg Cantors (1967) 4

  5. An Overview • Born: March 3, 1845 in St. Petersburg, Russia • 1856: Moved to Frankfurt • 1863: University of Berlin • 1869: Faculty at University of Halle • 1874: Married Vally Guttmann • Had six children • 1884: First hospitalization • 1899: Second hospitalization • 1918: Death 5

  6. 1874-1884: Towards a theory of Sets • On a Property of the Collection of All Real Algebraic Numbers(1874) • Set Theory has nontrivial content • There are infinitely many possible sizes for infinite sets • The device of one-to-one correspondence 6

  7. Contributions to the Founding of the Theory of Transfinite Numbers (1915) • Smallest transfinite cardinal number: Aleph-null • Developed an arithmetic of transfinite numbers • Continuum hypothesis 7

  8. References • Georg Cantor : his mathematics and philosophy of the infinite / Joseph Warren Dauben, Princeton, N.J. : Princeton University Press, 1990. • http://academic.eb.com/levels/collegiate/article/20082 • https://en.wikipedia.org/wiki/Georg_Cantor 8

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