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

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Presentation transcript:

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 “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

Cantor's Biography: An even more controversial topic E.T. Bell's Men of Mathematics (1937) Lack of access to unpublished documents Adolf Fraenkel's obituary (1930) Probleme des Unendlichen: Werk und Leben Georg Cantors (1967) 4

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

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

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

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