János Bolyai
János Bolyai  

Portrait of J. Bolyai by Ferenc Márkos (2012)^{[1]}


Born 
Kolozsvár (Klausenburg), Transylvania, Habsburg Empire (now ClujNapoca, Romania) 
15 December 1802
Died 
27 January 1860 Marosvásárhely, Transylvania, Austrian Empire (now Târgu Mureş, Romania) 
(aged 57)
Residence  Habsburg Empire, Austrian Empire 
Nationality  Hungarian 
Fields  Mathematics 
Academic advisors  Farkas Bolyai 
Known for  NonEuclidean geometry 
János Bolyai (Hungarian: ; 15 December 1802 – 27 January 1860) or Johann Bolyai,^{[2]} was a Hungarian mathematician, one of the founders of nonEuclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines. 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.^{[3]}
Contents
 Early life 1
 Career 2
 Personal life 3
 Legacy 4
 References 5
 Sources 6
 External links 7
Early life
Bolyai was born in the Transylvanian town of Kolozsvár (Klausenburg), then part of Hungary in the Habsburg Empire (now ClujNapoca in Romania), the son of Zsuzsanna Benkő and the wellknown mathematician Farkas Bolyai.
By the age of 13, he had mastered calculus and other forms of analytical mechanics, receiving instruction from his father. He studied at the Royal Engineering College in Vienna from 1818 to 1822.
Career
He became so obsessed with Euclid's parallel postulate that his father wrote to him: "For God's sake, I beseech you, give it up. Fear it no less than sensual passions because it too may take all your time and deprive you of your health, peace of mind and happiness in life". 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.
He wrote to his father: "I created a new, different world out of nothing."^{[1]}
Between 1820 and 1823 he prepared a treatise on a complete system of nonEuclidean geometry. Bolyai's work was published in 1832 as an appendix to a mathematics textbook by his father.
Gauss, on reading the Appendix, wrote to a friend saying "I regard this young geometer Bolyai as a genius of the first order". In 1848 Bolyai discovered that Lobachevsky had published a similar piece of work in 1829. Though Lobachevsky published his work a few years earlier than Bolyai, it contained only hyperbolic geometry. Bolyai and Lobachevsky did not know each other or each other's works.
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 Bolyai–Teleki library in Marosvásárhely (today Târgu Mureş), where Bolyai died.
Personal life
He was an accomplished polyglot speaking nine foreign languages, including Chinese and Tibetan. He learned the violin and performed in Vienna.“  It is related of him that he was challenged by thirteen officers of his garrison, a thing not unlikely to happen considering how differently he thought from everyone else. He fought them all in succession – making it his only condition that he should be allowed to play on his violin for an interval between meeting each opponent. He disarmed or wounded all his antagonists. It can be easily imagined that a temperament such as his was not one congenial to his military superiors. He was retired in 1833.^{[4]}  ” 
No original portrait of Bolyai survives. An unauthentic picture appears in some encyclopedias and on a Hungarian postage stamp.^{[1]}
Legacy
The BabeşBolyai University in ClujNapoca, that was established in 1959, bears his name, as does the crater Bolyai on the Moon^{[5]} and the János Bolyai Mathematical Institute at the University of Szeged. Furthermore, 1441 Bolyai, a minor planet discovered in 1937, is named after him; and many primary and secondary schools in the Carpathian Basin bear his name, e.g. Bolyai János Műszaki Szakközépiskola in Budapest, Bolyai János Gyakorló Általános Iskola és Gimnázium in Szombathely, Bolyai János Általános Iskola in Debrecen, etc. A street in Budapest, Hungary and another one in Timișoara, Romania is also named after him. The professional society of Hungarian mathematicians also bears his name.
There is also a mathematical award given out every five years named the Bolyai Prize.
References
 ^ ^{a} ^{b} ^{c} ^{d}
 ^ Tucker McElroy. A to Z of Mathematicians
 ^ Encyclopedia Britannica: János Bolyai
 ^ Sources cited, p. 41. Entire chapter V, "The Second Chapter in the History of Four Space", pp. 4160, provides accessible, illustrated, introduction to his life and work.
 ^ NASA website
Sources
 Martin Gardner, NonEuclidean Geometry, Chapter 4 of The Colossal Book of Mathematics, W.W.Norton & Company, 2001, ISBN 0393020231
 M. J. Greenberg, Euclidean and NonEuclidean Geometries: Development and History, 3rd edition, W. H. Freeman, 1994
 Elemér Kiss: Mathematical gems from the Bolyai chests. János Bolyai's discoveries in number theory and algebra as recently deciphered from his manuscripts. Translated by Anikó Csirmaz and Gábor Oláh. Akadémiai Kiadó, Budapest; TypoTeX, Budapest, 1999. 200 pp. ISBN 9630575639;
 Tibor Weszely: János Bolyai. Die ersten 200 Jahre, Birkhäuser, 2013 (translated from Hungarian by Manfred Stern), ISBN 9783034600460
 (Romanian) A. Todea, F. Maria, M. Avram, Oameni de știință mureșeni  Dicționar biobibliografic, CJ Mureș Biblioteca Județeană Mureș, tipografia Mediaprint SRL, 2004
External links
 Media related to at Wikimedia Commons
 .
 János Bolyai at the Mathematics Genealogy Project
 The Bolyai Memorial Museum