Euclid's decline
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While Gauss leaves only a few notes and letters about his research, fearing the "outcry of the Boeotians", the Hungarian János Bolyai (1802–1860) has no such hesitation: in 1829, he writes a short, twenty-four-page treatise in Latin (then Hungary's official language), which his father Farkas incorporates into his masterpiece, the Tentamen. "Out of nothing, I have created a strange new world", the younger Bolyai writes to his father at just 21. A little later, and independently, Nikolai Lobachevsky (1792–1856) publishes his theory of parallels in a series of papers.
Each of Europe's three major language families—Slavic, Romance and Germanic—thus played a part in this revolution, but works written in Russian and Hungarian reached few readers. Non-Euclidean geometry finally began to flourish only in 1866, thanks to the remarkable translation and outreach work of the French mathematician Jules Hoüel.
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Beltrami's maps
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