Editing 1963 in science (section)

==Mathematics==
* [[Paul Cohen]] uses [[Forcing (mathematics)|forcing]] to prove that the [[continuum hypothesis]] and the [[axiom of choice]]  are [[Independence (mathematical logic)|independent]] from [[Zermelo–Fraenkel set theory]].
* [[Walter Feit]] and [[John G. Thompson]] state the [[Feit–Thompson theorem]].<ref>{{cite journal|last1=Feit|first1=Walter|last2=Thompson|first2=John G.|title=Solvability of groups of odd order|url=http://projecteuclid.org/Dienst/UI/1.0/Journal?authority=euclid.pjm&issue=1103053941|mr=0166261|year=1963|journal=[[Pacific Journal of Mathematics]]|volume=13|issue=3|pages=775–1029|doi=10.2140/pjm.1963.13.775|doi-access=free}}</ref>
* [[Edward Lorenz]] publishes his discovery of the '[[butterfly effect]]', significant in the development of [[chaos theory]].<ref>{{cite journal|last=Lorenz|first=Edward N.|title=Deterministic Nonperiodic Flow|journal=[[Journal of the Atmospheric Sciences]]|date=March 1963|volume=20|issue=2|pages=130–141|doi=10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2|bibcode=1963JAtS...20..130L|doi-access=free}}</ref>
* [[Atiyah–Singer index theorem]] announced by [[Michael Atiyah]] and [[Isadore Singer]].<ref>{{cite journal|last1=Atiyah|first1=Michael F.|last2=Singer|first2=Isadore M.|title=The Index of Elliptic Operators on Compact Manifolds|journal=[[Bulletin of the American Mathematical Society]]|volume= 69|pages=422–433|year=1963|doi=10.1090/S0002-9904-1963-10957-X|issue=3|doi-access=free}}</ref>