The fourth dimension

42 THE FOURTH DIMENSION.

closely connected with his name, but a study of his writings shows that he was a man capable of carrying on mathematics in its main lines of advance, and of a judgment equal to discerning what these lines were. Appointed rector of his University, he died at an advanced age, surrounded by friends, honoured, with the results of his beneficent activity all around him. To him no subject came amiss, from the foundations of geometry to the improvement of the stoves by which the peasants warmed their houses.

He was born in 1793. His scientific work was unnoticed till, in 1867, Houel, the French mathematician, drew attention to its importance.

Johann Bolyai de Bolyai was born in Klausenburg, a town in Transylvania, December 15th, 1802.

His father, Wolfgang Bolyai, a professor in the Reformed College of Maros Vasarhely, retained the ardour in mathematical studies which had made him a chosen companion of Gauss in their early student days at Gottingen.

He found an eager pupil in Johann. He relates that the boy sprang before him like a devil. As soon as he had enunciated a problem the child would give the solution and command him to go on further. As a thirteen-year-old boy his father sometimes sent him to fill his place when incapacitated from taking his classes. The pupils listened to him with more attention than to his father for they found him clearer to understand.

In a letter to Gauss Wolfgang Bolyai writes:—

“My boy is strongly built. He has learned to recognise many constellations, and the ordinary figures of geometry. He makes apt applications of his notions, drawing for instance the positions of the stars with their constellations. Last winter in the country, seeing Jupiter he asked: ‘How is it that we can see him from here as well as from