Einfacher Beweis und Verallgemeinerung des Fundamentaltheorems für die biquadratischen Reste (+) Geometrischer Beweis des Fundamentaltheorems für die quadratischen Reste.

Berlin, G. Reimer, 1844. 4to. In ""Journal für die reine und angewandte Mathematik, 28 Band, 3. Heft, 1844"". In the original printed wrappers, without backstrip. Last leaf with repair. Fine and clean. [Eisenstein:] Pp. 223-245"" Pp. 246-247. [Entire issue: 193-288, (2), + two folded plates.]

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First printing of two important papers by the German mathematics prodigy Eisenstein. Even though he died prematurely at the age of 29, he managed to prove biquadratic reciprocity, Quartic reciprocity, Cubic 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 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)