János Bolyai | |
|---|---|
.jpg) Portrait by Ferenc Márkos (2012)[1] | |
| Born | (1802-12-15)15 December 1802 |
| Died | 27 January 1860(1860-01-27) (aged 57) |
| Education | TherMilAk (diploma, 1822) |
| Known for | Non-Euclidean geometry |
| Scientific career | |
| Fields | Mathematics |
| Academic advisors | Farkas Bolyai |
János Bolyai (/ˈbɔːljɔɪ/;[2]Hungarian:[ˈjaːnoʃˈboːjɒi]; 15 December 1802 – 27 January 1860) orJohann Bolyai,[3] was aHungarianmathematician who developedabsolute geometry—a geometry that includes bothEuclidean geometry andhyperbolic geometry. 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.[4]
Bolyai was born in the town of Kolozsvár,Grand Principality of Transylvania (nowCluj-Napoca inRomania), the son of Zsuzsanna Benkő and the well-known mathematicianFarkas Bolyai.
By the age of 13, he had masteredcalculus and other forms ofanalytical mechanics, receiving instruction from his father. He studied at theImperial and Royal Military Academy (TherMilAk) inVienna from 1818 to 1822, and Bolyai received his commission as sub-lieutenant. At the age of 21, he was already a lieutenant, at the age of 22, a first lieutenant and at the age of 24, a captain.[5]
Bolyai became so obsessed withEuclid'sparallel postulate that his father, who had pursued the same subject for many years, wrote to him in 1820: "You must not attempt this approach to parallels. I know this way to the very end. I have traversed this bottomless night, which extinguished all light and joy in my life. I entreat you, leave the science of parallels alone...Learn from my example."[6]
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. In 1823, he wrote to his father: "I have discovered such wonderful things that I was amazed...out of nothing I have created a strange new universe."[6][7] Between 1820 and 1823 he had prepared a treatise onparallel lines that he calledabsolute geometry. Bolyai's work was published in 1832 as an appendix to a mathematics textbook by his father.
Carl Friedrich Gauss, on reading the Appendix, wrote in a letter, "I regard this younggeometer Bolyai as a genius of the first order."[8] To his old friend Farkas Bolyai, however, Gauss wrote: "To praise it would amount to praising myself. For the entire content of the work...coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years."[9][6][8][7] Indeed, Gauss had disclosed his discovery of a consistent non-Euclidean geometry in a letter in 1827, and in 1829 wrote that he feared backlash if he published about it.[10] János suspected that Gauss had been secretly informed about his discoveries by his father, causing a rift between him and his father.[11] He later bitterly complained about Gauss's attitude.[12]
In 1848 Bolyai learned thatNikolai Ivanovich Lobachevsky had published a piece of work similar to his appendix in 1829. Though Lobachevsky published his work a few years earlier than Bolyai, it contained onlyhyperbolic geometry. Working independently, Bolyai and Lobachevsky pioneered the investigation ofnon-Euclidean geometry.
In addition to his work in geometry, Bolyai developed a rigorous geometric concept ofcomplex numbers as ordered pairs ofreal 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 theTeleki-Bolyai Library inTârgu Mureș, where Bolyai died. His grave lies in the Lutheran Cemetery in Târgu Mureș.[13]
He was an accomplished linguist, speaking several foreignlanguages beside his native Hungarian, these beingGerman,Latin,French,Italian andRomanian. He learned the violin and performed in Vienna.[14]
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.[15]
No original portrait of Bolyai survives. An unauthentic picture appears in some encyclopedias and on a Hungarian postage stamp.[1]
TheBabeș-Bolyai University inCluj-Napoca, that was established in 1959, bears his name, as does the professional society of Hungarian mathematicians, theJános Bolyai Mathematical Institute, at theUniversity of Szeged. There is also a mathematical award given out every five years, named theBolyai Prize. Bolyai is a minor character in the 1969 science-fiction/fantasy story"Operation Changeling", where his unique abilities allow the protagonists to navigate the non-Euclidean geometry ofHell.[citation needed]
The craterBolyai on theMoon[16] and1441 Bolyai, aminor planet discovered in 1937, are also named after him.
Several primary and secondary schools in theCarpathian Basin also bear Bolyai's name; for instance, Bolyai János Műszaki Szakközépiskola inBudapest, Bolyai János Gyakorló Általános Iskola és Gimnázium inSzombathely, and the Bolyai János Általános Iskola inDebrecen.[citation needed] Streets in Budapest, Cluj-Napoca,[17] andTimișoara[18] are named after Bolyai.
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Media related toJános Bolyai at Wikimedia Commons
