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Lack of access to unpublished documents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. 8