János Bólyai (1802-1860) was a Hungarian mathematician. He was the son of Farkas Bolyai, another mathematician, who was a friend and colleague of the great German mathematician Carl Friedrich Gauss. János Bólyai invented non-Euclidean geometry at the same time as and independently of his rival, the Russian mathematician and astronomer Nikolai Lobachevsky. Bolyai's work focused on the construction of what is now known as hyperbolic geometry. Bolyai's greatest work was carried out while he was still a teenager.