"THERE HAVE BEEN ONLY THREE EPOCH-MAKING MATHEMATICIANS: ARCHIMEDES, NEWTON, AND EISENSTEIN"

EISENSTEIN, G. [GOTTHOLD].

Théorèmes sur les Formes cubiques et Solution d'une Equation du quatrième Degré à quatre indéterminées (+) Über die Anzahl der quadratischen Formen, welche in der Theorie der complexen Zahlen zu einer reellen Determinante gehören (+) Allgemeine Auflösung der Gleichungen von den ersten vier Graden (+) Untersuchungen über die cubischen Formen mit zwei Variabeln (+) Über eine merkwürdige identische Gleichung (+) Bemerkungen zu den elliptischen und Abelschen Transcendenten (+) Transformations remarquables de quelques séries (+) Beiträge zur Kreistheilung (+) Elementare Ableitung einer merkwürdigen Relation zwischen zwei unendlichen producten (+) Beweis des Reciprocitätssatzes für die cubischen Reste in der Theorie der aus dritten Wurzeln der Einheit zusammengesetzten complexen Zahlen (+) Über die Anzahl der quadratischen Formen in den verschiedenen complexen Theorien (+) Einfacher Algorithmus zur Bestimmung des Werthes von (a/b). Beteiligte Personen und Organisationen (+) Eigenschaften und Beziehungen der Ausdrücke, welche bei der Auflösung der allgemeinen cubischen Gleichungen erscheinen (+) Neuer und elementarer Beweis des Legendreschen Reciprocitäts-Gesetzes.

Berlin, G. Reimer, 1844. 4to. In contemporary half cloth. In "Journal für die reine und angewandte Mathematik", 27. band, Heft 1-4, 1844. Entire volume 27 offered. A small library stamp to lower part of p. 1 and a white label pasted on to upper part of spine. Light occassional brownspotting, otherwise fine and clean.

First printing of these influential papers by the German mathematics prodigy Eisenstein. Even though he died prematurely at the age of 29, he managed to prove Cubic reciprocity (presented in the present papers) biquadratic reciprocity, Quartic reciprocity, to be imprisoned by the Prussian army for revolutionary activities in Berlin and making Gauss state that: "There have been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein". Alexander von Humboldt, then 83, accompanied Eisenstein's remains to the cemetery. The papers presented in the present issue is among his most prominent and made him famous throughout the mathematical world. (James, Driven to innovate, P. 88).

"The twenty-seventh (the present and most extensive) and twenty-eighth volumes of Crelle's Journal, published in 1844, contained twenty-five contributions by Eisenstein. These testimonials to his almost unbelievable, explosively dynamic productivity rocketed him to fame throughout the mathematical world. They dealt primarily with quadratic and cubic forms, the reciprocity theorem for cubic residues, fundamental theorems for quadratic and biquadratic residues, cyclotomy and forms of the third degree, plus some notes on elliptic and Abelian transcendentals. Gauss, to whom he had sent some of his writings, praised them very highly and looked forward with pleasure to an announced visit. In June 1844, carrying a glowing letter of recommendation from Humboldt, Eisenstein went off to see Gauss. He stayed in Göttingen fourteen days. In the course of the visit he won the high respect of the "prince of mathematicians," whom he had revered all his life. The sojourn in Göttingen was important to Eisenstein for another reason: he became friends with Moritz A. Stern-the only lasting friendship he ever made. While the two were in continual correspondence on scientific matters, even Stern proved unable to dispel the melancholy that increasingly held Eisenstein in its grip. Even the sensational recognition that came to him while he was still only a third-semester student failed to brighten Eisenstein's spirits more than fleetingly. In February 1845, at the instance of Ernst E. Kummer, who was acting on a suggestion from Jacobi (possibly inspired by Humboldt), Eisenstein was awarded an honorary doctorate in philosophy by the School of Philosophy of the University of Breslau.

Eisenstein soon became the subject of legend, and the early literature about him is full of errors. His treatises were written at a time when only Gauss, Cauchy, and Dirichlet had any conception of what a completely rigorous mathematical proof was. Even a man like Jacobi often admitted that his own work sometimes lacked the necessary rigor and self-evidence of methods and proofs." (DSB).

Order-nr.: 48885