Why Eisenstein Proved the Eisenstein Criterion and Why Schönemann Discovered It First

@article{Cox2011WhyEP,
  title={Why Eisenstein Proved the Eisenstein Criterion and Why Sch{\"o}nemann Discovered It First},
  author={David A. Cox},
  journal={The American Mathematical Monthly},
  year={2011},
  volume={118},
  pages={21 - 3}
}
  • David A. Cox
  • Published 1 January 2011
  • Mathematics
  • The American Mathematical Monthly
Abstract 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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