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Georg
Cantor 1845
- 1918
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 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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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...
This site also includes:
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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...
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This short biography is by Eric W. Weisstein,
offering links to different aspects of Cantor's mathematical theories.
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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...
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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..."
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This etext is available from the School
of Mathematics, Trinity
College, Dublin
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