Riemann's

Indeed, Helmholtz claimed that he had come to results similar to Riemann's, though perhaps slightly later.

Hermann von Helmholtz Patton, Lydia 2008

Riemann's Habilitationsrede, given 10 June 1854, “On the Hypotheses Underlying Geometry,” published posthumously by Dedekind, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, volume 13

Hermann von Helmholtz Patton, Lydia 2008

Riemann's work revolutionized mathematics and physics, and philosophy by extension, and Helmholtz was perhaps the first to recognize the extent of the revolution.

Hermann von Helmholtz Patton, Lydia 2008

Although the publication of Riemann's Habilitationsrede,

Hermann von Helmholtz Patton, Lydia 2008

The difference in the titles, facts versus hypotheses, underscores the fact that while Helmholtz's approach is very similar to Riemann's, there is at least one significant difference.

Hermann von Helmholtz Patton, Lydia 2008

Helmholtz's title, “On the Facts Underlying Geometry,” is a deliberate echo of Riemann's “On the Hypotheses Underlying Geometry.”

Hermann von Helmholtz Patton, Lydia 2008

Less a representation of geometric form than of the integral of a Riemann's sum, Got Lost reminds me of that stage of night when I've enjoyed a good fifties era bar a bit too much.

Picture Envy #20 – Creative Matrices 2005

Consider the modern formulation of Riemann's theory in this

Nineteenth Century Geometry Torretti, Roberto 2007

Less a representation of geometric form than of the integral of a Riemann's sum, Got Lost reminds me of that stage of night when I've enjoyed a good fifties era bar a bit too much.

unbillable hours: 2005

In Erastosthene's and Riemann's time, there was no Internet.

The Speculist: The Trouble With String Theory 2006