Friederich Pius Philipp Furtwängler (21 April 1869 to 19 May 1940) was a German number theorist. He wrote an 1896 doctoral dissertation at the University of Göttingen on cubic forms under Felix Klein, and spent most of his academic life, from 1912 to 1938, at the University of Vienna, where he taught Kurt Gödel, who later said Furtwängler's lectures on number theory were the best mathematical lectures he ever heard. From 1916 he was increasingly paralysed and lectured from a wheelchair while an assistant wrote the equations on the blackboard. He is best known for his 1929 contribution to the principal ideal theorem.
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Most of his academic life, from 1912 to 1938, was spent at the University of Vienna, where he taught for example Kurt Gödel, who later said that Furtwängler's lectures on number theory were the best mathematical lectures that he ever heard; Gödel had originally intended to become a physicist but turned to mathematics partly as a result of Furtwängler's lectures.
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This result was proved by Philipp Furtwängler (1929).
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