Article ID: CBB001211029

Why Eisenstein Proved the Eisenstein Criterion and Why Schönemann Discovered It First (2011)


This article explores the history of the Eisenstein irreducibility criterion and explains how Theodor Schönemann discovered this criterion before Eisenstein. Both were inspired by Gauss's Disquisitiones Arithmeticae, though they took very different routes to their discoveries. The article will discuss a variety of topics from 19th-century number theory, including Gauss's lemma, finite fields, the lemniscate, elliptic integrals, abelian groups, the Gaussian integers, and Hensel's lemma.

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Authors & Contributors
Ehrhardt, Caroline
Craik, Alex D. D.
Kaçar, Mustafa
Bir, Atilla
Lützen, Jesper
Grabiner, Judith V.
British Society for the History of Mathematics Bulletin
Historia Mathematica
American Mathematical Monthly
Osmanli Bilimi Arastirmalari: Studies in Ottoman Science
Science in Context
History and Philosophy of Logic
American Mathematical Society
Cambridge University Press
Galois, Évariste
Steiner, Jakob
Ekinci, Salih Zeki
Lagrange, Joseph Louis
Poincaré, Jules Henri
Bolzano, Bernard
Time Periods
19th century
18th century
20th century, early
Paris (France)
Ottoman Empire
Zurich (Switzerland)
Great Britain
Académie des Sciences, Paris

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