Bolyai was educated by his father, famed mathematician Farkas (Wolfgang) Bolyai, in Marosvásárhely and by the time he was 13 had mastered calculus and other forms of analytical mechanics. Bolyai also was an accomplished violinist and was an accomplished linguist speaking nine foreign languages including Chinese and Tibetan. He received military training and studied at the Imperial Engineering Academy in Vienna from 1818 to 1822. Immediately after this he joined the army engineering corps in which he spent 11 years. In 1820 he began to work in a direction that ultimately led him to a non-Euclidean geometry. In 1823, after vain attempts to prove the Euclidean parallel postulate (Given any straight line and a point not on it, there “exists one and only one straight line which passes” through that point and never intersects the first line), he developed his system by assuming that a geometry could be constructed without the parallel postulate. Although his theory of absolute space opened new horizons in mathematics, physics, and even in philosophy it was only published as an appendix to his father’s book on mathematics.
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