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Georg Cantor (1845 - 1918)

Go BackGerman Philosophy, Mathematician, Philosopher of the Infinite
 
 Georg Cantor : His Mathematics and Philosophy of the Infinite Georg Cantor : His Mathematics and Philosophy of the Infinite by Joseph Warren Dauben

"Historians of mathematics can only be grateful for the effort Professor Dauben has expended to create the synthesis of Cantor scholarship found in this book. But the book can, and I hope will, be read with profit by a far more extensive audience. Any student, mathematician, philosopher, theologian, or general historian with an interest in Georg Cantor and the wondrous revolution in mathematical and philosophical thought that his work did so much to precipitate will find this book of considerable interest."--Thomas Hawkins, Historia Mathematica One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important study the most thorough yet written of the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula. Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.

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Georg Ferdinand Ludwig Philipp Cantor -- Biography

This fairly detailed Georg Cantor biography is from the School of Mathematics and Statistics at the University of St Andrews, Scotland.  This is the home of the MacTutor History of Math Archives.

Excerpt:

...While at Berlin Cantor became much involved with the Mathematical Society being president of the Society during 1864-65. He was also part of a small group of young mathematicians who met weekly in a wine house. After receiving his doctorate in 1867, Cantor taught at a girl's school in Berlin. Then, in 1868, he joined the Schellbach Seminar for mathematics teachers. During this time he worked on his habilitation and, immediately after being appointed to Halle in 1869, he presented his thesis, again on number theory, and received his habilitation...

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Georg Cantor -- Biography (Archived)

This biography is by Paul Golba

Excerpt:

Georg Cantor put forth the modern theory on infinite sets that revolutionized almost every mathematics field. However, his new ideas also created many dissenters and made him one of the most assailed mathematicians in history...

 

Georg Cantor -- Biography 

This short biography is by Eric W. Weisstein, offering links to different aspects of Cantor's mathematical theories.

 

Georg Cantor -- Biography (Archived)

This short Cantor biography is by J. W. Dauben 

Excerpt:

Georg Ferdinand Ludwig Philipp Cantor, b. Mar. 3, 1845, d. Jan. 6, 1918, was a Russian-born German mathematician best known as the creator of SET THEORY and for his discovery of the transfinite numbers. He also advanced the study of trigonometric series, was the first to prove the nondenumerability of the real numbers, and made significant contributions to dimension theory...

 

Cantor set and function

This essay is by Alexander Bogomolny.  Bogomolny begins:

"A continuous function may grow considerably virtually without changing. The function with this property is easily constructed on the  Cantor set C0. So I'll proceed in two steps..."

 

Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen (1872)

This etext is available from the School of Mathematics, Trinity College, Dublin

 

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