Promises

from: Rossana Tazzioli, RIEMANN - Le géomètre de la nature, Belin pour la science,2010.

I have been enjoying the above mentionned book on Riemann and have found the findings, cited in the box, quite interesting. The book goes on to mention that a few years earlier, Gauss had announced this finding, adding that he would eventually produce a proof- «of childlike simplicity» but never did. Promises, promises.

Clearly the idea is preposterous in the Cartesian plane: the integral is the area under the curve, so that the oddity has to come from the play of calculations when the y axisis i. What would a function definition look like on the complex plane anyway. The plane is itself a function of sorts.

The book hints that the function is harmonic...