Cantor Defeated Galileo in the Battle of Infinite Numbers


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Who was Georg Cantor?

Georg Cantor: Photographer unknown

Georg Cantor was born in St. Petersburg, Russia in March of 1845. His father, a merchant, saw to his education with a private tutor at home, primary school in St. Petersburg, the Wiesbaden Gymnasium (or senior secondary school), and eventually the Realschule in Darmstadt for engineering and the Polytechnic of Zurich for mathematics.

Educating Georg Cantor

His father had pushed Georg into engineering, but consented to the switch to mathematics. Following his father’s death, Cantor studied in Berlin and Göttingen. He completed his dissertation in 1867 and took up teaching mathematics.

The Infinities of Georg Cantor

Cantor proved that the rational numbers, or fractions, had a one-to-one relationship with integers in 1873. The next year, he published a paper showing that real numbers did not share that property, the very topic discussed in this article.

Other Aspects of Georg Cantor’s Life and Work

In 1874, Cantor also proved that it is possible to associate a finite line segment’s points with all the points of a finite square. Three years later, he showed a similar correspondence between a line segment’s points and points in a finite p-dimensional space.

Cantor pursued, but did not resolve, the question of whether the cardinality of real numbers was the very next infinity after the cardinality of integers. He did significant work on transfinite numbers and set theory; lectured at university; sparked ideas in other mathematicians by personal correspondence and through organizations. He is considered a father of set theory.

He was also deeply interested in the philosophy of mathematics, as well as the theory that Francis Bacon was the author of Shakespeare’s works.

He was married and fathered six children. He also suffered from depression, particularly in his later life.

Georg Cantor died in Halle, Germany in January of 1918.


Hrbacek, Karel and Jech, Thomas. “Introduction to Set Theory”. (Third Edition, 1999). Quoted in {Jech, Thomas. “Basic Set Theory“. Stanford Encyclopedia of Philosophy. (2002)}. Accessed Sept. 10, 2011.
O’Connor, J.J. and Robertson, E.F. “Georg Ferdinand Ludwig Philipp Cantor”. University of St. Andrews, Scotland. (Oct. 1998). Accessed Sept. 10, 2011.

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