Article ID: CBB001211029

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

unapi

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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https://data.isiscb.org/isis/citation/CBB001211029/

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Authors & Contributors
Craik, Alex D. D.
Reich, Karin
Abeles, Francine F.
Angelelli, Ignacio A.
Bir, Atilla
Callison, Mary Joan
Journals
Historia Mathematica
American Mathematical Monthly
British Society for the History of Mathematics Bulletin
Logica Universalis
Archive for History of Exact Sciences
History and Philosophy of Logic
Publishers
Cambridge University Press
Edition am Gutenbergplatz Leipzig
Princeton University Press
Shaker
Concepts
Mathematics
Mathematicians
Proof
Geometry
Logic
Functions (mathematics)
People
Abel, Niels Henrik
al-Kāshī, Jamshīd Ibn Maḥmūd Ghyāth al-Dīn
Appel, Kenneth
Bartels, Martin
Bolzano, Bernard
Carlini, Francesco
Time Periods
19th century
18th century
20th century
20th century, early
Ancient
Qajar dynasty, Iran (1794-1925)
Places
Paris (France)
Great Britain
India
Iran
Mesopotamia
Ottoman Empire
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