Bolyai, Janos

The native form of this personal name is Bolyai János. This article uses the Western name order.

János Bolyai
Unauthentic fantasy portrait of Bolyai
Born	15 December 1802(1802-12-15) Klausenburg, Transylvania, Habsburg Empire
Died	27 January 1860(1860-01-27) (aged 57) Neumarkt am Mieresch, Transylvania, Habsburg Empire
Residence	Habsburg Empire
Fields	Mathematics
Known for	non-Euclidean geometry

János Bolyai (pronounced [ˈjaː.noʃ ˈboː.jɒ.i]) (December 15, 1802 – January 27, 1860) was a Hungarian mathematician, known for his work in non-Euclidean geometry.

Bolyai was born in the Transylvanian town of Klausenburg, then part of the Habsburg Empire (now Cluj-Napoca in Romania), the son of Zsuzsanna Benkö and the well-known mathematician Farkas Bolyai.

Contents 1 Life 2 Other work 3 Legacy 4 References 5 External links

[edit] Life

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. 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".^[1] 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 not only that Lobachevsky had published a similar piece of work in 1829, but also a generalization of this theory. As far as is known, Lobachevsky published his work a few years earlier than Bolyai, but it contained only hyperbolic geometry. Bolyai and Lobachevsky did not know each other or each other's works.

[edit] Other work

In addition to his work in the 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.

He was an accomplished polyglot speaking nine foreign languages, including Chinese and Tibetan. 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.

[edit] Legacy

The Babeş-Bolyai University in Cluj-Napoca, that was established in 1959, bears his name, as does the crater Bolyai on the Moon ^[2] 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.

[edit] References

[edit] External links

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, http://www-history.mcs.st-andrews.ac.uk/Biographies/Bolyai.html .
• János Bolyai at the Mathematics Genealogy Project
• The Bolyai Memorial Museum

Persondata
Name	Bolyai, Janos
Alternative names
Short description
Date of birth	December 15, 1802
Place of birth	Kolozsvár, Transylvania, Habsburg Empire
Date of death	January 27, 1860
Place of death	Marosvásárhely, Transylvania, Habsburg Empire