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
Ehrhardt, Caroline
Anne van Weerden
Sacchetti, Andrea
Chang, Ping-Ying
Lorenat, Jemma
Dauben, Joseph W.
Concepts
Mathematics
Mathematicians
Proof
Geometry
Science and society
Logic
Time Periods
19th century
18th century
Qing dynasty (China, 1644-1912)
Ancient
20th century, early
17th century
Places
France
China
Paris (France)
Zurich (Switzerland)
Ottoman Empire
Mesopotamia
Institutions
Astronomical Bureau (China)
Académie des Sciences, Paris
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