Bolyai became so obsessed with
Euclid's
parallel postulate that his father, who had pursued the same subject for many years, wrote to him in 1820: "You must not attempt this approach to parallels. I know this way to the very end. I have traversed this bottomless night, which extinguished all light and joy in my life. I entreat you, leave the science of parallels alone...Learn from my example." János, however, persisted in his quest and eventually came to the conclusion that the postulate is independent of the other axioms of geometry and that different consistent geometries can be constructed on its negation. In 1823, he wrote to his father: "I have discovered such wonderful things that I was amazed...out of nothing I have created a strange new universe." To his old friend Farkas Bolyai, however, Gauss wrote: "To praise it would amount to praising myself. For the entire content of the work...coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years." János suspected that Gauss had been secretly informed about his discoveries by his father, causing a rift between him and his father. He later bitterly complained about Gauss's attitude. In 1848 Bolyai learned that
Nikolai Ivanovich Lobachevsky had published a piece of work similar to his appendix in 1829. Though Lobachevsky published his work a few years earlier than Bolyai, it contained only
hyperbolic geometry. Working independently, Bolyai and Lobachevsky pioneered the investigation of
non-Euclidean geometry. In addition to his work in geometry, Bolyai developed a rigorous geometric concept of
complex numbers as ordered pairs of
real numbers. Although he never published more than the 24 pages of the Appendix, he left more than 20,000 pages of mathematical manuscripts when he died. These can now be found in the
Teleki-Bolyai Library in
Târgu Mureș, where Bolyai died. His grave lies in the Lutheran Cemetery in Târgu Mureș. ==Personal life==