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János Bolyai
János Bolyai (; 15 December 1802 – 27 January 1860) or Johann Bolyai,〔Tucker McElroy. (''A to Z of Mathematicians'' )〕 was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world.〔(Encyclopedia Britannica: János Bolyai )〕 ==Early life== Bolyai was born in the Transylvanian town of Kolozsvár (Klausenburg), then part of Hungary in the Habsburg Empire (now Cluj-Napoca in Romania), the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai. By the age of 13, he had mastered calculus and other forms of analytical mechanics, receiving instruction from his father. He studied at the Royal Engineering College in Vienna from 1818 to 1822.
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