I hope you’ve enjoyed this web presentation as much as I enjoyed putting it together. While this is the end of the line for now, there is much, much more to discover, both about the many topics raised here (naturally!), and also about Riemann himself. Please join in the work! Here are some references to set yourself out on a good track of discoveries. And, it's always more fun with a team!

References

Complex magnitudes

• Gauss’s 1799 doctoral dissertation demonstrated the physical reality of complex numbers (also called imaginary numbers), and formed the basis for the early development of the LaRouche Youth Movement. See also Bruce Director's “Bringing the Invisible to the Surface”
• Caspar Wessel’s On the Analytical Representation of Direction is a very fun approach to complex magnitudes, and formed the basis of the geometric means of dealing with them on this site. It is available as a book published by The Royal Danish Academy of Sciences and Letters, and an excerpt, covering everything we touched on in this site, is available in the Source Book of Mathematics, published by Dover. A new translation of the relevant sections will appear here when it is completed.

Dirichlet's Principle

• Gauss's work on potential: General Propositions Relating to Attractive and Repulsive Forces Acting in the Inverse Ratio of the Square of the Distance

Riemann's Work

• Riemann's 1851 Theory of Functions of a Complex Variable (his doctoral dissertation) was where he first introduced Riemann surfaces.
• Riemann's 1854 habilitation dissertation, On the Hypotheses that Underlie Geometry of 1854 was the subject of an animated video presentation.
• His 1857 Theory of Abelian Functions (part 1 · part 2) was also the subject of an LPACTV video (part 1 · part 2)
• Kendrick Press has released a translation of Bernhard Riemann's Collected Papers.
• Various of Riemann’s “Philosophical Fragments,” translated by an LPAC team, are available as well. They include some of his thoughts on life and mind.

Contact

Feedback? Questions? Suggestions? Additions? Let me know what you think. You can contact me at: [email protected]

— Jason Ross