János Bolyai

János Bolyai [ja ː noʃ bojɒi ] (* December 15, 1802 in Cluj, † January 17, 1860 in Tirgu Mures ), formerly the German Johann Bolyai was a Hungarian mathematician. He worked as one of the first mathematicians in the field of non-Euclidean geometry.

Life

János Bolyai was the son of Farkas Wolfgang Bolyai, a professor of mathematics. Bolyai's own talent in mathematics and languages ​​and music was up early. At seven, he learned violin, made rapid progress and entered later in Vienna publicly as a violinist on. He received mathematics instruction from his father and attended only nine years from a school, the Calvinist College in Tirgu Mures, where his father taught.

After leaving school in 1817 he began studying engineering at the Vienna Military Academy. The actual required mathematics study abroad could not afford the family; his father's request to his friend Carl Friedrich Gauss to receive the son as a student, had received a negative decision. János Bolyai received his engineering degree in 1822 and devoted himself successfully, a year later scientific studies. He initially as his father trying to prove the parallel postulate of Euclid, and developed through the examination of the foundations of Euclidean geometry then basic features of a non-Euclidean geometry. About some problems, he exchanged in this time with his friend Carl Szasz (1798-1835) made ​​, but in 1821 went as a teacher to Hungary.

In 1823 János Bolyai engineer officer in the imperial army ( second lieutenant ), where he initially cooperated with the fortifications of Temesvár to 1826. In the army he was an excellent swordsman known as well for his abstinence - he did not drink, did not smoke and kept well away from the game. 1826 to 1830 he was stationed in Arad, after 1830, initially in Lviv. In 1827 he was lieutenant and lieutenant commander in 1832.

He developed his ideas on non-Euclidean geometry in his military further, but remained isolated and was able to convince them of the importance of his work only on a visit in 1831 and his father. This then urged on a publication as an appendix in his own work " Tentamen ". The Father sent his book also Gaussian, although it recognized the importance in a response letter and praised the power of the Son - literally, he wrote, to have been surprised, " utmost " - at the same time but told to have made ​​this discovery for themselves what for János Bolyai was a heavy blow. He suspected at times even his father, an old college friend of Gauss, to have betrayed this from his previous releases something.

Bolyai, who was stationed from 1832 in Olomouc, now suffered from poor health. There were hypochondria and choleric inclinations according to his service record. His superiors recognized the high mathematical ability, but criticized frequent Kränklichkeiten, lack of inclination to the engineering activity and tendency to isolation of the fellow officers and konstatierten a distinct passion for the game of chess. In 1833, retire Bolyai, having previously in 1832 in vain - had asked for a three-year leave of absence in order to devote himself to mathematics - with reference to the letter of Gauss.

János Bolyai then lived on the family estate at Domáld together with Rozalia Kibedi Orban ( Orban Rosalia of Kibed ), with whom he had two children; because the costs borne sum of money was missing, the marriage took place only in 1849. The marriage, which faced his father is adverse, did not last long - in 1852 the couple separated. Bolyai dealt further with mathematics, for example, he submitted a price work in Leipzig on the role of complex numbers in geometry. In 1846 he moved to the vicinity of his father's Marosvásárhely. There he learned in 1848 the work of Lobachevsky non-Euclidean geometry to know. Most recently, he was mainly concerned with philosophy and left a large estate to manuscripts that are in the Bolyai - Teleki library in Tirgu Mures. János Bolyai died in January 1860 of pneumonia in Tirgu Mures.

Like his father worked at J. Bolyai research on the axiom of parallels. However, he was one of the first alongside Carl Friedrich Gauss and Lobachevsky Nikolai Ivanovich a non-Euclidean geometry, an " absolutely true ( hyperbolic ) geometry of space ".

Little known is its derived from mathematics philosophy whose basic idea can be reconstructed only from fragments of his treatise on the soul, matter and spirit, as well as his letter to Emperor Franz Josef, among other practical proposals for a new, more equitable financial order contains. The huge estate Bolyai has been deciphered in decades of work Elemér Kiss.

After Victor Babeş and give him the Babeş -Bolyai University of Cluj was named. At the mathematician also remind the asteroid ( 1441 ) Bolyai and since 1970 a lunar crater.

From Bolyai there are no portraits - the only portrait destroyed Bolyai himself with a saber. An often copied image that also appeared on stamps for his 100th anniversary in 1960 in Hungary and Romania is not authentic, but probably shows an unknown contemporaries; it is a painting by Mór Adler (1826-1902) modeled from 1864, but that made no information about the person depicted. Lühnsdorf Károly (1893-1958) made ​​it a drawing and listed incorrectly, that it was a portrait of Janos Bolyai. The only representation that can possibly lay claim to authenticity, is a bust in front of the Palace of Culture of Tirgu Mures, made ​​around 1911, when the son Dénes Bolyai (then a retired judge) and other people who knew him, that is still alive. But there are authentic portraits of his father, his mother and his son, were tried that in the 1990s reconstructions of the approximate appearance of Bolyai, for example, by the painter Attila Zsigmond.