János Bolyai

Born: 15 Dec 1802 Died: 27 Jan 1860

János Bolyai was a Hungarian mathematician, known for his work in non- Euclidean geometry.

Bolyai was born in Kolozsvár, Transylvania, Kingdom of Hungary, Habsburg Empire, today Cluj-Napoca, Romania, he was son of Zsuzsanna Benko and of a well-known mathematician, Farkas Bolyai, but soon went to Marosvásárhely where his father had a job at the Calvinist College teaching mathematics, physics and chemistry, therefore Farkas Bolyai always wanted that its son was a mathematician.

It was clear from early on, however, that János was an extremely bright and observant child: when he was four he could distinguish certain geometrical figures, knew about the sine function, and could identify the best known constellations. To the five years he had learn, practically by himself, to read. When he was 13, he had mastered the calculus and other forms of analytical mechanics.

His father had an obsession with the status of Euclid's famous parallel postulate and devoted his life to trying to prove it. Despite his father's warnings that it would ruin his health, peace of mind, and happiness, Janos too started working on this axiom until, in about 1820, he came to the conclusion that it could not be proved. He went on to develop a consistent geometry in which the parallel postulate is not used, thus establishing the independence of this axiom.

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 an essay 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 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 20000 pages of manuscript of mathematical manuscripts. These are now in the Bolyai- Teleki Library in Morosvásáhely , now Târgu-Mures, Romania.

Singular personality, was skiççful violinist and excellent skilled. He was an accomplished polyglot speaking nine foreign languages including Chinese and Tibetan. Hedied at the age of 58, in January 1860.

Citation

“Out of nothing I have created a strange new universe“ – Janós Bolyai 1

Sources

MacTutor History of Mathematics archive [On line]. St Andrews : University of St Andrews, 2006. [Consult. 28 Out. 2009]. Available in WWW: .

Wikipedia [On line]. [s.l.] : Wikipedia Foundation, [s.d.], mod. 31 Ag. 2009. [Consult. 26 Out. 2009]. Available in WWW: .

Answers.Com [On line]. [s.l.] : Answers Corporation, 2009. [Consult. 27 Out. 2009]. Available in WWW:

Portal EmDiv [On line]. Minas : Portal EmDiv, cop. 2009. [Consult. 28 Out. 2009]. Available in WWW:

Available books in the Mathematical Library

János Bolyai Appendix : the theory of space. - Amsterdam : North-Holland, 1987. - 238 p. - (North-Holland mathematics studies ; 138)

51-03/BOL.Jan

Non-euclidean geometry . - New York : Dover, [1955]. - XII, 268 p.

51-03/BON/ex.1

51-03/BON/ex.2

János Bolyai, non-euclidean geometry, and the nature of space / Jeremy J. Gray. - Cambridge, Mas. : Burndy Library, distributed by the MIT Press, 2004. - IV, [p.var.] : il.. - (Burndy library publications. new series ; 1)

51-03/BOL

La science absolue de l'espace . - Paris : Hermann, 1912. - 64 p.

CAVE-51-03/BOL.Sci

1 Reference to the creation of a non-Euclidean geometry