Publication and Non-Reception up to 1855
In the 1830s Ferdinand Minding described a surface of revolution with constant negative curvature. He showed that figures can be moved around freely on it, but made no connection to non-Euclidean geometry. In the 1840s the Bolyais found out about Lobachevskii’s work, which they generally liked, but they did not get in touch with him. The most notable contact was Gauss’s reply to the Appendix written by János Bolyai, where Gauss famously claimed that to praise it would be to praise himself. This reply contributed to a painful separation between the Bolyais, and convinced János that there was no point in publishing again. Gauss’s praise for Lobachevskii went more smoothly. Gauss nominated him for membership of the Göttingen Academy of Sciences and praised him among his small circle of friends, but otherwise did nothing to promote his work. Only after Gauss died and his endorsement of non-Euclidean geometry could be traced in the papers he left behind did the reception of the new geometry change. By then both János Bolyai and Lobachevskii were dead.
KeywordsConstant Curvature Geodesic Segment Constant Negative Curvature Pleasant Surprise Spherical Trigonometry
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