Portrait of J. Bolyai by Ferenc Márkos (2012)
15 December 1802|
Kolozsvár, Transylvania, Habsburg Empire (now Cluj-Napoca, Romania)
|Died||27 January 1860
Marosvásárhely, Transylvania, Austrian Empire (now Târgu Mureş, Romania)
|Residence||Habsburg Empire, Austrian Empire|
|Known for||Non-Euclidean geometry|
János Bolyai (Hungarian: [ˈjaː.noʃ ˈboː.jɒ.i]) (15 December 1802 – 27 January 1860) was a Hungarian mathematician, one of the founders of non-Euclidean 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.
Early life 
Bolyai was born in the Transylvanian town of Kolozsvár (Klausenburg), then part of the Habsburg Empire (now Cluj-Napoca in Romania), the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai.
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: "Out of nothing I have created a strange new universe".
Between 1820 and 1823 he prepared a treatise on a complete system of non-Euclidean 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 Târgu Mureş, where Bolyai died.
Personal life 
No original portrait of Bolyai survives. An unauthentic picture appears in some encyclopedias and on a Hungarian postage stamp.
The Babeş-Bolyai University in Cluj-Napoca, that was established in 1959, bears his name, as does the crater Bolyai on the Moon 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 high schools in the Carpathian Basin bear his name.
There is also a mathematical award given out every five years named the Bolyai Prize.
- Dénes, Tamás (January 2011). "Real Face of János Bolyai" (PDF). Notices of the American Mathematical Society 58 (1): 41–51. Retrieved 18 June 2011.
- Encyclopedia Britannica: János Bolyai
- Lines, Malcolm E. (1994). On the Shoulders of Giants. Bristol: Institute of Physics Pub. ISBN 0-7503-0103-1.
- NASA website
- Martin Gardner, Non-Euclidean Geometry, Chapter 4 of The Colossal Book of Mathematics, W.W.Norton & Company, 2001, ISBN 0-393-02023-1
- M. J. Greenberg, Euclidean and Non-Euclidean 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 963-05-7563-9;
- Tibor Weszely: János Bolyai. Die ersten 200 Jahre, Birkhäuser, 2013 (translated from Humgarian by Manfred Stern), ISBN 978-3-0346-0046-3
|Wikimedia Commons has media related to: János Bolyai|
- O'Connor, John J.; Robertson, Edmund F., "János Bolyai", MacTutor History of Mathematics archive, University of St Andrews.
- János Bolyai at the Mathematics Genealogy Project
- The Bolyai Memorial Museum