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==Mathematics== * [[Inductive dimension#Relationship between dimensions|Menger-Nöbeling theorem]]. * [[John von Neumann]] makes foundational contributions to [[ergodic theory]] in a series of papers.<ref>{{cite journal|first=John|last=von Neumann|title=Proof of the Quasi-ergodic Hypothesis|year=1932|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|volume=18|pages=70–82|doi=10.1073/pnas.18.1.70|pmid=16577432|issue=1|pmc=1076162|bibcode=1932PNAS...18...70N |doi-access=free}}</ref><ref>{{cite journal|first=John|last=von Neumann|title=Physical Applications of the Ergodic Hypothesis|year=1932|journal=Proceedings of the National Academy of Sciences of the United States of America|volume=18|pages=263–266|doi=10.1073/pnas.18.3.263|pmid=16587674|issue=3|pmc=1076204|jstor=86260|bibcode=1932PNAS...18..263N|doi-access=free}}</ref><ref>{{cite journal|authorlink=Paul Halmos|quote=if von Neumann had never done anything else, they would have been sufficient to guarantee him mathematical immortality.|title=Von Neumann on Measure and Ergodic Theory|first=Paul R.|last=Halmos|journal=[[Bulletin of the American Mathematical Society]]|volume=64|issue=3|year=1958|pages=86–94|doi=10.1090/s0002-9904-1958-10203-7|doi-access=free|url=https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-64/issue-3.P2/Von-Neumann-on-measure-and-ergodic-theory/bams/1183522373.pdf}}</ref> * [[Rózsa Péter]] presents the results of her paper on [[recursive function theory]], "Rekursive Funktionen," to the [[International Congress of Mathematicians]] in Zurich, Switzerland. * December – [[Marian Rejewski]] of the [[Poland|Polish]] [[Biuro Szyfrów]] applies pure mathematics – [[permutation group]] theory – to breaking the [[Wehrmacht|German armed forces]]' [[Enigma machine]] ciphers.<ref>{{cite book|authorlink=David Kahn (writer)|first=David|last=Kahn|title=The Codebreakers|edition=2nd|year=1996|page=974}}</ref><ref>{{cite book|last=Kozaczuk|first=Władysław|authorlink=Władysław Kozaczuk|year=1984|title=Enigma: How the German Machine Cipher was Broken, and how it was Read by the Allies in World War Two|location=Frederick, Md|publisher=University Publications of America|isbn=978-0-89093-547-7|pages=234–236}}</ref>
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