Editing 1901 in science (section)

==Mathematics==
* April – [[Henri Lebesgue]] defines [[Lebesgue integration]] for some function f(x).<ref>''[[Comptes rendus de l'Académie des Sciences]]''.</ref>
* May/June – [[Russell's paradox]]: [[Bertrand Russell]] shows that [[Georg Cantor]]'s [[naive set theory]] leads to a contradiction.<ref>{{cite book|url=https://books.google.com/books?id=Xg6QpedPpcsC&pg=PA350|last=Griffin|first=N.|chapter=The Prehistory of Russell's Paradox|title=One Hundred Years of Russell's Paradox: mathematics, logic, philosophy|editor=Link, Godehard|page=350|year=2004|isbn=978-3-11-017438-0}}</ref>
* [[Élie Cartan]] develops the [[exterior derivative]].
* [[Leonard Eugene Dickson]] publishes ''Linear groups with an exposition of the Galois field theory'' in [[Leipzig]], advancing the [[classification of finite simple groups]] and listing almost all [[Non-abelian group|non-abelian]] [[simple group]]s having order less than one billion.<ref>{{cite journal|last=Parshall|first=K. H.|year=1991|title=A study in group theory: Leonard Eugene Dickson's Linear groups|journal=Mathematical Intelligencer|volume=13|pages=7–11|authorlink=Karen Parshall|doi=10.1007/bf03024065}}</ref>
* [[Aleksandr Lyapunov]] proves the [[central limit theorem]] rigorously using characteristic functions.<ref>{{cite book|first=Tony|last=Crilly|title=50 Mathematical Ideas you really need to know|location=London|publisher=Quercus|year=2007|isbn=978-1-84724-008-8|page=141}}</ref>