Editing 1796 in science (section)

==Mathematics==
* This is a productive year for the [[German people|German]] mathematician [[Carl Friedrich Gauss]] (born [[1777 in science|1777]]) and his work in [[number theory]]:<ref>{{cite book|last=Dunnington|first=G. Waldo|title=Carl Friedrich Gauss: Titan of Science|location=Washington, DC|publisher=Mathematical Association of America|edition=new|year=2004|isbn=978-0-88385-538-6|oclc=53933110}}</ref><ref>{{cite book|last=Hall|first=Tord|title=Carl Friedrich Gauss: a Biography|location=Cambridge, MA|publisher=MIT Press|year=1970|isbn=978-0-262-08040-8|oclc=185662235|url-access=registration|url=https://archive.org/details/carlfriedrichgau00tord}}</ref>
** March 30 – He obtains conditions for the constructibility by ruler and compass of regular [[polygon]]s, including the [[heptadecagon]].<ref>{{cite book|first=Carl Friedrich|last=Gauss|chapter=§§365–366|title=Disquisitiones Arithmeticae|location=Leipzig|year=1801|title-link=Disquisitiones Arithmeticae}}</ref>
** April 8 – He becomes the first to prove the [[quadratic reciprocity]] law, enabling determination of the solvability of any [[quadratic equation]] in [[modular arithmetic]].
** May 31 – He puts forward his [[prime number theorem]] on the distribution of [[prime number]]s among the integers.
** July 10 – He discovers that every positive integer is representable as a sum of at most three [[triangular numbers]], noting in his diary "[[Eureka (word)|Heureka]]! num&nbsp;=&nbsp;Δ&nbsp;+&nbsp;Δ&nbsp;+&nbsp;Δ."
** October 1 – He publishes a result on the number of solutions of [[polynomial]]s with [[coefficient]]s in [[finite field]]s.
* [[Adrien-Marie Legendre]] conjectures the [[prime number theorem]].