20th century

=== Mathematics ===
[[File:Alan Turing portré.jpg|thumb|upright|The pioneer of [[computer science]], [[Alan Turing]]]]

Multiple new fields of mathematics were developed in the 20th century. In the first part of the 20th century, [[measure theory]], [[functional analysis]], and [[topology]] were established, and significant developments were made in fields such as [[abstract algebra]] and [[probability]]. The development of [[set theory]] and [[formal logic]] led to [[Gödel's incompleteness theorems]].

Later in the 20th century, the development of computers led to the establishment of a [[theory of computation]].<ref name="BoyerMath">{{Cite book|title=A history of mathematics|last=Boyer|first=Carl B.|date=1991|publisher=Wiley|others=[[Uta Merzbach|Merzbach, Uta C.]], 1933–, Rogers D. Spotswood Collection.|isbn=978-0471543978|edition=2nd ed. [rev.]|location=New York|oclc=23823042|url=https://archive.org/details/historyofmathema00boye}}</ref> Computationally-intense results include the study of [[fractal]]s<ref>{{cite book|last1=Devaney|first1=Robert L.|title=A first course in chaotic dynamical systems : theory and experiment|date=1998|publisher=Addison-Wesley|location=Reading, Mass. [u.a.]|isbn=978-0-201-55406-9|edition=6. printing.}}</ref> and a proof of the [[four color theorem]] in 1976.<ref>{{Cite journal|title=Every Planar Map is Four-Colorable|date=26 July 1976|journal=Bulletin of the American Mathematical Society|author1=Kenneth Appel|author2-link=Wolfgang Haken|author2=Wolfgang Haken |series=Contemporary Mathematics|volume=98|doi=10.1090/conm/098|isbn=9780821851036|s2cid=8735627|url=http://projecteuclid.org/euclid.bams/1183538218|author1-link=Kenneth Appel}}</ref>