Editing 1837 in science (section)

==Mathematics==
* [[Peter Gustav Lejeune Dirichlet]] publishes [[Dirichlet's theorem on arithmetic progressions]], using [[mathematical analysis]] concepts to tackle an algebraic problem and thus creating the branch of [[analytic number theory]]. In proving the theorem, he introduces the [[Dirichlet character]]s and [[Dirichlet L-function|L-functions]].<ref>{{cite book|last1=Kanemitsu|first1=Shigeru|first2=Chaohua|last2=Jia|title=Number Theoretic Methods: future trends|year=2002|publisher=Springer|isbn=978-1-4020-1080-4|pages= 271–274}}</ref><ref>{{cite book|last=Gowers|first=Timothy|author2=Barrow-Green, June|author3=Leader, Imre|title=The Princeton Companion to Mathematics|year=2008|publisher=Princeton University Press|isbn=978-0-691-11880-2|pages=764–765}}</ref> He also notes the difference between the [[Absolute convergence|absolute]] and [[conditional convergence]] of [[Series (mathematics)|series]] and its impact in what will later be called the [[Riemann series theorem]].
* [[Bernard Bolzano]] publishes ''Wissenschaftslehre''.
* [[William Rowan Hamilton]] treats [[complex number]]s as [[ordered pair]]s of [[real number]]s.<ref name=Crilly>{{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}}</ref>
* [[Siméon Denis Poisson]]'s lectures on probability (introducing [[Poisson distribution]]) and decision theory are published.<ref>{{cite book|first=S.-D.|last=Poisson|title=Probabilité des jugements en matière criminelle et en matière civile, précédées des règles générales du calcul des probabilitiés|location=Paris|publisher=Bachelier|year=1837|url=https://archive.org/details/recherchessurla01poisgoog|quote=recherches sur la probabilité des jugements en matière criminelle.}}</ref>
* [[Pierre Wantzel]] proves that several ancient [[geometric]] problems (including [[doubling the cube]] and [[trisecting the angle]]) are impossible to solve using only [[compass and straightedge]].<ref name=Crilly/><ref>{{cite journal|first=L.|last=Wantzel|title=Recherches sur les moyens de reconnaître si un problème de géométrie peut se résoudre avec la règle et le compas|journal=Journal de Mathématiques Pures et Appliquées|year=1837|volume=1|pages=366–372|url=http://visualiseur.bnf.fr/ConsulterElementNum?O=NUMM-16381&Deb=374&Fin=380&E=PDF}}</ref>