
The Abel–Ruffini Theorem: Complex but Not Complicated
Ramond, Paul (2022), The Abel–Ruffini Theorem: Complex but Not Complicated, The American Mathematical Monthly, 129, 3, p. 231-245. 10.1080/00029890.2022.2010494
View/ Open
Type
Article accepté pour publication ou publiéDate
2022Journal name
The American Mathematical MonthlyVolume
129Number
3Pages
231-245
Publication identifier
Metadata
Show full item recordAbstract (EN)
In this article, using only elementary knowledge of complex numbers, we sketch a proof of the celebrated Abel–Ruffini theorem, which states that the general solution to an algebraic equation of degree five or more cannot be written using radicals, that is, using its coefficients and arithmetic operations +,−,×,÷, and √. The present article is written purposely with concise and pedagogical terms and dedicated to students and researchers not familiar with Galois theory, or even group theory in general, which are the usual tools used to prove this remarkable theorem. In particular, the proof is self-contained and gives some insight as to why formulae exist for equations of degree less than five (and how they are constructed), and why they do not for degree five or more.Related items
Showing items related by title and author.
-
Keppler, Jan-Horst (2007) Chapitre d'ouvrage
-
Ruiz-Tagle, Jaime; Sehnbruch, Kirsten (2015) Article accepté pour publication ou publié
-
Robert, Christian P.; Gelman, Andrew (2013) Article accepté pour publication ou publié
-
Lépinette, Emmanuel; Zhao, Jun (2020) Article accepté pour publication ou publié
-
Ramond, Olivier; Escaffre, Lionel (2007) Communication / Conférence