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Georg Cantor

Georg Cantor. Emre Alpagut CMPE.220 / Dr. Haluk Bingöl 15/11/2016. 1. “In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi.”. 2. Cantor: A controversial figure. “scientific charlatan, renegade, acorrupter of youth” - Leopold Kronecker

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Georg Cantor

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 Cantor's Biography: An even more controversial topic • E.T. Bell's Men of Mathematics (1937) • Lack of access to unpublished documents • Adolf Fraenkel's obituary (1930) • Probleme des Unendlichen: Werk und Leben Georg Cantors (1967) 4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