Commentatio mathematica...

By Bernhard Riemann

An essay of Bernhard Riemann

Commentatio mathematica, qua respondere tentatur quaestioni ab Illma Academia Parisiensi propositae:
``Trouver quel doit être l'état calorifique d'un corps solide homogène indéfeni pour qu'un système de courbes isothermes, à un instant donné, restent isothermes après un temps quelconque, de telle sorte que la température d'un point puisse s'exprimer en fonction du temps et de deux autres variables indépendantes.''
published in Bernhard Riemann's Gesammelte Matheamtische Werke, edited by Heinrich Weber (2nd Edition, Teubner 1892, pp. 391-404), is available here in the following formats:

This essay was submitted to the Paris Academy in 1861, to compete for a prize relating to the conduction of heat. The second part of this essay contains some of the mathematical analysis underlying Riemann's inaugural lecture Ueber die Hypothesen, welche der Geometrie zu Grunde liegen on the foundations of Geometry. A translation into English of an extract from this part of the essay is to be found in Volume II of A Comprehensive Introduction to Differential Geometry by Michael Spivak (2nd Edition, Publish or Perish Inc, Berkeley, 1979, vol. II, pp. 179-182).


D.R. Wilkins
School of Mathematics
Trinity College, Dublin