Editing 1843 in science (section)

==Mathematics==
* September – [[Ada Lovelace]] translates and expands [[Luigi Federico Menabrea|Menabrea]]’s notes on [[Charles Babbage]]'s [[analytical engine]], including an [[algorithm]] for calculating a sequence of [[Bernoulli numbers]], regarded as the world's first [[computer program]].<ref>{{cite journal|first1=John|last1=Fuegi|first2=Jo|last2=Francis|s2cid=40077111|title=Lovelace & Babbage and the creation of the 1843 'notes'|journal=[[IEEE Annals of the History of Computing]]|volume=25|issue=4|pages=16–26|doi=10.1109/MAHC.2003.1253887|date=October–December 2003}}</ref><ref>{{cite web|url=http://cs-www.cs.yale.edu/homes/tap/Files/ada-bio.html|title=Ada Byron, Lady Lovelace|access-date=2010-07-11|archive-url=https://web.archive.org/web/20100721013509/http://cs-www.cs.yale.edu/homes/tap/Files/ada-bio.html|archive-date=21 July 2010|url-status=live}}</ref><ref>{{cite journal|last=Menabrea|first=L. F.|author-link=Luigi Federico Menabrea|year=1843|title=Sketch of the Analytical Engine Invented by Charles Babbage|journal=[[Scientific Memoirs]]|volume=3|url=http://www.fourmilab.ch/babbage/sketch.html|access-date=2010-10-01|archive-url=https://web.archive.org/web/20100913042032/http://www.fourmilab.ch/babbage/sketch.html|archive-date=13 September 2010|url-status=live}}</ref>
* October 16 – [[William Rowan Hamilton]] discovers the calculus of [[quaternions]] and deduces that they are non-commutative.<ref>{{cite web|title=William Rowan Hamilton Plaque|url=https://www.geograph.org.uk/photo/347941|work=Geograph|year=2007|access-date=2011-03-08}}</ref>
* [[Arthur Cayley]] and [[James Joseph Sylvester]] found the algebraic [[invariant theory]].
* [[John T. Graves]] discovers the [[octonion]]s.
* [[Pierre-Alphonse Laurent]] discovers and presents the Laurent expansion theorem.