I am reading The Value of Science by Poincare, and the following paragraph from Chapter I seems rather interesting:
Look at Professor Klein: he is studying one of the most abstract questions of the theory of functions to determine whether on a given Riemann surface there always exists a function admitting of given singularities. What does the celebrated German geometer do? He replaces his Riemann surface by a metallic surface whose electric conductivity varies according to certain laws. He connects two of its points with the two poles of a battery. The current, says he, must pass, and the distribution of this current on the surface will define a function whose singularities will be precisely those called for by the enunciation.
Poincare makes this observation when comparing two different types of mathematical minds and Klein, according to him, is of the intuitive type.
I do not know much about Riemann surfaces but I am very curious what problem Klein was working on. How could he solve an abstract problem using conductivity and battery? The book gives no reference to this paragraph.