Янош Боляй: Абсолютті геометрияның негізін қалаушы математик

Hungarian mathematician (1802–1860)

[[File:Bolyai arckép. JPG|thumb|János Bolyai; artwork by Attila Zsigmond was a Hungarian mathematician who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world.

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.

He was an accomplished linguist speaking several foreign languages: German, Latin, French, Italian, Romanian. He learned the violin and performed in Vienna. No original portrait of Bolyai survives. An unauthentic picture appears in some encyclopedias and on a Hungarian postage stamp. and 1441 Bolyai, a minor planet discovered in 1937, are also named after him. Several primary and secondary schools in the Carpathian Basin also bear Bolyai's name; for instance, Bolyai János Műszaki Szakközépiskola in Budapest, Bolyai János Gyakorló Általános Iskola és Gimnázium in Szombathely, and the Bolyai János Általános Iskola in Debrecen. Streets in Budapest, Cluj Napoca, and Timișoara are named after Bolyai.

"Appendix scientiam spatii absolute veram exhibens; a veritate aut falsitate axiomatis XI Euclidei, a priori haud unquam", appendix to Farkas Bolyai, Tentamen juventutem studiosam in elementa matheseos purae, elementaris ac sublimioris, methodo intuitiva, evidentiaque huic propria, introducendi (An Attempt to Introduce Studious Youths to the Elements of Pure Mathematics), 1832. English translation: "The Science Absolute of Space: Independent of the Truth or Falsity of Euclid's Axiom XI (Which Can Never Be Decided A Priori)", The Neomon, Austin, 1896.