Editing Emmy Noether (section)

===Historical context===
In the century from 1832 to Noether's death in 1935, the field of mathematics – specifically [[algebra]] – underwent a profound revolution whose reverberations are still being felt. Mathematicians of previous centuries had worked on practical methods for solving specific types of equations, e.g., [[cubic function|cubic]], [[quartic equation|quartic]], and [[quintic equation]]s, as well as on the [[root of unity|related problem]] of constructing [[regular polygon]]s using [[compass and straightedge constructions|compass and straightedge]]. Beginning with [[Carl Friedrich Gauss]]'s 1832 proof that [[prime number]]s such as five can be [[integer factorization|factored]] in [[Gaussian integer]]s,<ref>{{cite journal |first=Carl F. |last=Gauss |author-link=Carl Friedrich Gauss |title=Theoria residuorum biquadraticorum – Commentatio secunda |year=1832 |language=la |journal=Comm. Soc. Reg. Sci. Göttingen |volume=7 |pages=1–34}} Reprinted in {{cite book |title=Werke |trans-title=Complete Works of C.F. Gauss |publisher=[[Georg Olms Verlag]] |location=Hildesheim |year=1973 |pages=93–148}}</ref> [[Évariste Galois]]'s introduction of [[permutation group]]s in 1832 (although, because of his death, his papers were published only in 1846, by Liouville), [[William Rowan Hamilton]]'s description of [[quaternion]]s in 1843, and [[Arthur Cayley]]'s more modern definition of groups in 1854, research turned to determining the properties of ever-more-abstract systems defined by ever-more-universal rules. Noether's most important contributions to mathematics were to the development of this new field, [[abstract algebra]].{{sfn|Noether|1987|p=168}}