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
studythe most thorough yet writtenof 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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