Farkas Bolyai spent his life in close correspondence with Gauss, reconsidering the foundations of mathematics and proving Euclidean axioms. He published at his own expense at the press of the College where he taught in Transylvania the Tentamen. As an appendix to his work he published the short essay written by his son Janos Bolyai, which was recognized by Gauss and Lobachevskii as one of the great original contributions to mathematics.