Our 50th meeting will be held on Friday-Saturday, January 30--31, 2026, at Northern Kentucky University. At this meeting, we will read the proof, published in 1824 by the young Norwegian mathematician Niels Henrik Abel (1802--1829), that settled the negative resolution of the general quintic equation, a problem that had stood for two-and-a-half centuries (since the great Italian algebraists had solved the cubic and quartic equations in the mid-1500s). We will find this proof in his paper, Démonstration de l'impossibité de la résolution algébrique des équations générales qui passent le quatrième degré (A proof of the impossibility of the algebraic solution of general equations that exceed the fourth degree), as published in his Oeuvres complètes (Christiana, 1839).
In addition, two allied works may be helpful to you in our study of this paper. One is the book Abel's Proof, by Peter Pesic (MIT Press, 2003); the other is a very recent article by Adrian Rice, 200 Years Ago: Abel’s Resolution of the Quintic Question, which appears in the Jan 2026 Notices of the AMS. (Rice published a somewhat briefer account of this story, Abel Answers the Question of the Quintic, in the June 2024 issue of Mathematics Today, a journal of the Institute for Mathematics and Its Applications.)
Submissions from 1824
A Proof of the Impossibility of the Algebraic Solution of General Equations that Exceed the Fourth Degree, Niels Henrik Abel
