Editing Bertrand Russell (section)

===Early career===
{{see also|Axiom of reducibility}}
Russell began his published work in 1896 with ''German Social Democracy'', a study in politics that was an early indication of his interest in political and social theory. In 1896 he taught German social democracy at the [[London School of Economics]].<ref name="LSE">{{Cite web |date=26 August 2015 |title=London School of Economics |url=https://www.lse.ac.uk/aboutLSE/keyFacts/nobelPrizeWinners/russell.aspx |archive-url=https://web.archive.org/web/20141015192808/https://www.lse.ac.uk/aboutLSE/keyFacts/nobelPrizeWinners/russell.aspx |archive-date=15 October 2014 |publisher=London School of Economics}}</ref> He was a member of the [[Coefficients (dining club)|Coefficients dining club]] of social reformers set up in 1902 by the [[Fabian Society|Fabian]] campaigners [[Sidney Webb|Sidney]] and [[Beatrice Webb]].<ref name="LettersPg16">{{Cite book |last=Russell |first=Bertrand |url=https://books.google.com/books?id=EayyTTpXL-QC&pg=PA16 |title=Yours Faithfully, Bertrand Russell: Letters to the Editor 1904–1969 |publisher=Open Court Publishing |year=2001 |isbn=0-8126-9449-X |editor-last=Ray Perkins |location=Chicago |page=16 |access-date=16 November 2007}}</ref>

He now started a study of the [[foundations of mathematics]] at Trinity. In 1897, he wrote ''An Essay on the Foundations of Geometry'' (submitted at the [[Fellow]]ship Examination of Trinity College) which discussed the [[Cayley–Klein metric]]s used for [[non-Euclidean geometry]].<ref>Russell, Bertrand (1897) ''An Essay on the Foundations of Geometry'', p. 32, re-issued 1956 by [[Dover Books]]</ref> He attended the first [[International Congress of Philosophy]] in Paris in 1900 where he met [[Giuseppe Peano]] and [[Alessandro Padoa]]. The Italians had responded to [[Georg Cantor]], making a science of [[set theory]]; they gave Russell their literature including the ''[[Formulario mathematico]]''. Russell was impressed by the precision of Peano's arguments at the Congress, read the literature upon returning to England, and came upon [[Russell's paradox]]. In 1903 he published ''[[The Principles of Mathematics]]'', a work on the foundations of mathematics. It advanced a thesis of [[logicism]], that mathematics and logic are one and the same.<ref>{{Cite web |title=Bertrand Russell, biography |url=http://nobelprize.org/nobel_prizes/literature/laureates/1950/russell-bio.html |access-date=23 June 2010 |publisher=Nobel Foundation |archive-date=4 June 2011 |archive-url=https://web.archive.org/web/20110604131349/http://nobelprize.org/nobel_prizes/literature/laureates/1950/russell-bio.html |url-status=live }}</ref>

At the age of 29, in February 1901, Russell underwent what he called a "sort of mystic illumination", after witnessing [[Alfred North Whitehead|Whitehead]]'s wife's suffering in an [[Angina pectoris|angina]] attack. "I found myself filled with semi-mystical feelings about beauty and with a desire almost as profound as that of the [[Buddha]] to find some philosophy which should make human life endurable", Russell would later recall. "At the end of those five minutes, I had become a completely different person."<ref>{{Cite book |last=Bertrand Russell |url=https://books.google.com/books?id=SlMrmmrNuEoC |title=Autobiography |publisher=Psychology Press |year=1998 |isbn=978-0-415-18985-9 |chapter=6: Principia Mathematica |access-date=7 January 2016 |archive-date=10 September 2024 |archive-url=https://web.archive.org/web/20240910140331/https://books.google.com/books?id=SlMrmmrNuEoC |url-status=live }}</ref>

In 1905, he wrote the essay "[[On Denoting]]", which was published in the philosophical journal ''[[Mind (journal)|Mind]]''. Russell was elected a [[List of Fellows of the Royal Society elected in 1908|Fellow of the Royal Society (FRS) in 1908]].<ref name="frs" /><ref name="Gallery" /> The three-volume ''[[Principia Mathematica]]'', written with Whitehead, was published between 1910 and 1913. This, along with the earlier ''The Principles of Mathematics'', soon made Russell world-famous in his field. Russell's first political activity was as the [[Independent Liberal]] candidate in the [[1907 Wimbledon by-election|1907 by-election]] for the [[Wimbledon (UK Parliament constituency)|Wimbledon constituency]], where he was not elected.<ref>{{cite book|editor1-last=Craig|editor1-first=F. W. S.|title=British Parliamentary Election Results: 1885–1918|date=1974|publisher=Macmillan Press|location=London|isbn=9781349022984}}</ref>

In 1910, he became a lecturer at the [[University of Cambridge]], Trinity College, where he had studied. He was considered for a fellowship, which would give him a vote in the college government and protect him from being fired for his opinions, but was passed over because he was "anti-clerical", because he was agnostic. He was approached by the Austrian engineering student [[Ludwig Wittgenstein]], who started undergraduate study with him. Russell viewed Wittgenstein as a successor who would continue his work on logic. He spent hours dealing with Wittgenstein's various [[phobia]]s and his bouts of despair. This was a drain on Russell's energy, but Russell continued to be fascinated by him and encouraged his academic development, including the publication of Wittgenstein's ''[[Tractatus Logico-Philosophicus]]'' in 1922.<ref name="Wittgenstein">{{Cite web |title=Russell on Wittgenstein |url=http://www.rbjones.com/rbjpub/philos/history/rvw001.htm |access-date=1 October 2011 |website=Rbjones.com}}</ref> Russell delivered his lectures on [[logical atomism]], his version of these ideas, in 1918, before the end of [[World War I]]. Wittgenstein was, at that time, serving in the Austrian Army and subsequently spent nine months in an Italian [[prisoner of war]] camp at the end of the conflict.