FROBENIUS THEOREM

CLEBSCH, RUDOLF FRIEDRICH ALFRED.

Ueber die simultane Integration linearer partieller Differentialgleichungen.

Berlin, Georg Reimer, 1866. 4to. In "Journal für die reine und angewandte Mathematik, 65. Band, 3 Heft, 1866". In the original printed wrappers, without backstrip. Front wrapper with a brown mark to top left corner, otherwise fine and clean. [Clebsch:] Pp. 257-268. [Entire issue: Pp. 189-292, (2)].

First printing of Clebsch's paper in which the Frobenius theorem was introduced.

Despite being named after Ferdinand Georg Frobenius, the theorem was first proven by Alfred Clebsch and Feodor Deahna. Deahna was the first to establish the sufficient conditions for the theorem, and Clebsch developed the necessary conditions. Frobenius is responsible for applying the theorem to Pfaffian systems, thus paving the way for its usage in differential topology.

"German mathematician whose work on algebraic geometry was considered the first and most fundamental work in that branch of mathematics. Clebsch also developed a brilliant interpretation of some of Georg Riemann's work on function theory and investigated some aspects of algebraic geometry using approaches that differed from convention, focusing on algebraic interpretations rather than geometrical ones. Clebsch also founded an important journal, Mathematische Annalen before his premature death at the age of 39." (Schlager, Science and Its Times, P. 267)

The issue also contain:
Cayley, Sur un cas particulier de la surface du quatrieme ordre avec seize points singuliers, P. 284-290.

Order-nr.: 45094