In the Laws, Plato's Athenian stranger laments that the Greek people's pervasive ignorance of the incommensurability of a line with a surface and a surface with a solid, had rendered them more like "guzzling swine" than true human beings. While the same lament can be sounded with respect to today's society, modern citizens must also include an understanding of those higher transcendentals which are the subject of Riemann's "Theory of Abelian Functions", if they are to avoid the lamentable fate of Plato's fellow Greeks.

On June 10, 1854, Bernhard Riemann shocked the world by stating the obvious:

New ideas, like people, come into this world naked. To effectively perform their mission, they must be provided with clothes. But unlike children who can speak for themselves, ideas must be dressed in words and images which, upon careful reflection, indicate how they were conceived. And though it would be a grave error to mistake a person's substance for his or her outward appearance, the spirit of an idea (which also cannot be captured by a superficial account of its form) can, nevertheless, be evoked by that form's animation.

"It is well known that scientific physics has existed only since the invention of the differential calculus," stated Bernhard Riemann in his introduction to his late 1854 lecture series posthumously published under the title, "Partial Differential Equations and their Applications to Physical Questions". For most of his listeners, Riemann's statement would have been fairly straight forward, for they understood the physical significance of Leibniz's calculus as it had percolated over the preceding sesquicentury through the work of Kaestner and Gauss.

In his revolutionary essay of 1857, {Theory of Abelian Functions}, Bernhard Riemann brought to light the deeper epistemological significance of the complex domain, through a new and bold application of a principle of physical action which he called, “Dirichlet’s Principle”.