During his lifetime, Gauss published only few results of his research on the problems of the fifth postulate. However, further investigations concerning his work made it clear that he was the first one to discover the "non-Euclidean" geometry and called it as such. He wrote a letter that was addressed to F.A. Taurinus (a fellow mathematician) on November 8, 1824 telling him the following: "[…] it is true that your demonstration of the proof that the sum of the three angles of a plane triangle cannot be greater than 180 is somewhat lacking in geometrical rigor […] I imagine that this problem has not engaged you very long. I have pondered it for over thirty years, and I do not believe that anyone can have given more thought to this second part but I, though I have never published anything on it. The assumption that the sum of the three angles is less than 180 leads to a curious geometry, quite different from ours (the Euclidean), but thoroughly consistent, which I have developed to my entire satisfaction […]" (Wolfe, 1945, p.46-47).
Reference: Wolf, H.E. (1945). Introduction to non-Euclidean geometry
n.d, n.t, google image, retrieved on 4/11/2009
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