"Fourteen years before Beltrami published... a greater than he had studied the whole of the non-Euclidean problem from a more lofty and difficult point of view. This was Bernhard Riemann, who offered to Gauss three topics for his projected trial lecture as Privatsozent at Göttingen. Gauss chose the most difficult, wondering what so young a man could make of such an arduous subject; he learned. ...'Ueber die Hypothesen welche der Geometrie su Grunde liegen' ...was read in 1854, but never published till 1868. Riemann's approach is far different from anything that anyone had tried previously. ...The modern theory of relativity, on its mathematical side, is merely an elaboration of Riemann's analysis."

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Added on April 10, 2026
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