Editing János Bolyai

{{Short description|Hungarian mathematician (1802–1860)}}
{{Redirect|Bolyai|the lunar crater|Bolyai (crater)}}
{{Hungarian name|Bolyai János}}
{{Use dmy dates|date=April 2017|cs1-dates=y}}
{{Infobox scientist
| name              = János Bolyai
| image             = Bolyai János (Márkos Ferenc festménye).jpg
| caption           = Portrait by Ferenc Márkos (2012)<ref name="amsNotices">{{Cite journal
  | last = Dénes
  | first = Tamás
  |date=January 2011
  | title = Real Face of János Bolyai
  | journal = [[Notices of the American Mathematical Society]]
  | volume = 58
  | issue = 1
  | pages = 41–51
  | url = https://www.ams.org/notices/201101/rtx110100041p.pdf
  | access-date = 18 June 2011}}</ref>
| birth_date        = {{birth date|1802|12|15|df=y}}
| birth_place       = [[Cluj-Napoca|Klausenburg]], [[Principality of Transylvania (1711–1867)|Grand Principality of Transylvania]], [[Habsburg Monarchy]] (today [[Cluj-Napoca]], [[Romania]])
| death_date        = {{death date and age|1860|01|27|1802|12|15|df=y}}
| death_place       = [[Târgu Mureș|Neumarkt am Mieresch]], [[Austrian Empire]] (today [[Târgu Mureș]], [[Romania]])
| citizenship       = 
| nationality       = <!--Deprecated per MOS:INFONAT-->
| education         = [[Theresian Military Academy|TherMilAk]] ([[diploma]], 1822)
| doctoral_advisor  = 
| academic_advisors = [[Farkas Bolyai]]
| doctoral_students = 
| notable_students  = 
| known_for         = [[Non-Euclidean geometry]]
| fields            = [[Mathematics]]
| awards            = 
| signature         = 
| footnotes         = 
}}
[[File:Bolyai-arckép.JPG|thumb|János Bolyai; artwork by Attila Zsigmond<ref name="amsNotices"/>]]
[[File:Janos Bolyai memorial plaque.jpg|thumb|Memorial plaque of János Bolyai in [[Olomouc]], [[Czech Republic]]]]

'''János Bolyai''' ({{IPAc-en|ˈ|b|ɔː|l||j|ɔɪ}};<ref>[http://www.dictionary.com/browse/bolyai "Bolyai"]. ''[[Random House Webster's Unabridged Dictionary]]''.</ref> {{IPA|hu|ˈjaːnoʃ ˈboːjɒi|lang}}; 15 December 1802 – 27 January 1860) or '''Johann Bolyai''',<ref>Tucker McElroy. [https://books.google.com/books?id=MiZIWtX9AJUC&pg=PA40 ''A to Z of Mathematicians'']</ref> was a [[Hungarian people|Hungarian]] [[mathematician]] who developed [[absolute geometry]]—a geometry that includes both [[Euclidean geometry]] and [[hyperbolic 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.<ref>[http://www.britannica.com/EBchecked/topic/72441/Janos-Bolyai Encyclopædia Britannica: János Bolyai]</ref>

==Early life==
[[File:Bolyai Janos szulohaza.jpg|thumb|The house in [[Cluj-Napoca]] where János Bolyai was born]]

Bolyai was born in the town of Kolozsvár, [[Grand Principality of Transylvania]] (now [[Cluj-Napoca]] in [[Romania]]), the son of Zsuzsanna Benkő and the well-known mathematician [[Farkas Bolyai]].

By the age of 13, he had mastered [[calculus]] and other forms of [[analytical mechanics]], receiving instruction from his father. He studied at the [[Theresian Military Academy|Imperial and Royal Military Academy]] (TherMilAk) in [[Vienna]] 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.<ref>{{cite web|url=https://kollegium.uni-miskolc.hu/aboutbolyai|title=About Bolyai|publisher=Miskolci Egyetem Bolyai Kollégium|access-date=22 October 2023}}</ref>

==Career==
Bolyai became so obsessed with [[Euclid]]'s [[parallel 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."<ref name=Ellenberg>{{cite book |last=Ellenberg |first=Jordan| author-link=Jordan Ellenberg |date=May 2014 |title=[[How Not to Be Wrong]] |location=[[New York City|New York, NY]] |publisher=[[Penguin Group]] |page=365 |isbn=978-0-14-312-753-6}}</ref>

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."<ref name="Ellenberg"/><ref name="Tóth_1965"/> Between 1820 and 1823 he had prepared a treatise on [[parallel lines]] that he called [[absolute 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 young [[geometer]] Bolyai as a genius of the first order."<ref name="St Andrews">{{MacTutor Biography|id=Bolyai}}</ref> 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."<ref>[https://archive.org/details/briefwechselzwi00gausgoog/page/n146/mode/2up Letter from Gauss to Farkas Bolyai from 6 March 1832]</ref><ref name="Ellenberg"/><ref name="St Andrews"/><ref name="Tóth_1965"/> 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.<ref>Greenberg 2008, p. 243-244</ref> János suspected that Gauss had been secretly informed about his discoveries by his father, causing a rift between him and his father.<ref>{{Cite journal |last=Osserman |first=Robert |date=2005 |title=Book Review: Non-Euclidean Geometry, and the Nature of Space. |url=https://www.ams.org/journals/notices/200509/rev-osserman.pdf |journal=Notices of the AMS |volume=52 |issue=9}}</ref> He later bitterly complained about Gauss's attitude.<ref>Greenberg 2008, p. 242</ref> 

In 1848 Bolyai learned that [[Nikolai 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 only [[hyperbolic geometry]]. Working independently, Bolyai and Lobachevsky pioneered the investigation of [[non-Euclidean geometry]].

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 [[Teleki Library|Teleki-Bolyai Library]] in [[Târgu Mureș]], where Bolyai died. His grave lies in the Lutheran Cemetery in Târgu Mureș.<ref>{{MacTutor|class=Extras|id=Bolyai_house_grave|title=Janos Bolyai's birth house and original grave}}</ref>

==Personal life==
He was an accomplished linguist, speaking several foreign [[language]]s beside his native Hungarian, these being [[German language|German]], [[Latin]], [[French language|French]], [[Italian language|Italian]] and [[Romanian language|Romanian]]. He learned the violin and performed in Vienna.<ref>Elemér, Kiss, [http://mek.oszk.hu/05300/05321/05321.pdf "Matematikai kincsek Bolyai János kéziratos hagyatékából"]</ref>

{{quote|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.<ref>{{cite book|last1=Hinton|first1=Charles Howard|author-link1=Charles Howard Hinton|title=The Fourth Dimension|date=1912|orig-year=1904|publisher=[[Allen & Unwin|G. Allen & Unwin Ltd.]]|location=London|page=46| url=https://archive.org/stream/fourthdimension00hintarch#page/46/}} Sources cited, p. 41. Entire chapter V, "The Second Chapter in the History of Four Space", pp. 41–60, provides accessible, illustrated introduction to his life and work.</ref>}}
 
No original portrait of Bolyai survives. An unauthentic picture appears in some encyclopedias and on a Hungarian postage stamp.<ref name=amsNotices />

==Legacy==
The [[Babeș-Bolyai University]] in [[Cluj-Napoca]], that was established in 1959, bears his name, as does the professional society of Hungarian mathematicians, the [[János Bolyai Mathematical Institute]], at the [[University of Szeged]]. There is also a mathematical award given out every five years, named the [[Bolyai Prize]]. Bolyai is a minor character in the 1969 science-fiction/fantasy story [[Operation Chaos (novel)|"Operation Changeling"]], where his unique abilities allow the protagonists to navigate the non-Euclidean geometry of [[Hell]].{{Citation needed|date=September 2022}}

The crater [[Bolyai (crater)|Bolyai]] on the [[Moon]]<ref>[http://lunar.arc.nasa.gov/printerready/science/geography_items/carters/craters_b.html NASA website] {{webarchive|url=https://web.archive.org/web/20051023083235/http://lunar.arc.nasa.gov/printerready/science/geography_items/carters/craters_b.html |date=23 October 2005 }}</ref> and [[1441 Bolyai]], a [[minor planet]] discovered in 1937, are also named after him. 

Several primary and secondary schools in the [[Pannonian Basin|Carpathian Basin]] also bear Bolyai's name; for instance, Bolyai János Műszaki Szakközépiskola in [[Budapest]], Bolyai János Gyakorló Általános Iskola és Gimnázium in [[Szombathely]], and the Bolyai János Általános Iskola in [[Debrecen]].{{Citation needed|date=October 2013}} Streets in Budapest, Cluj-Napoca,<ref>{{cite web|url=https://www.clujeni.com/despre/strada_bolyai_janos/|title=Strada Bolyai Janos|website=www.clujeni.com|lang=ro|access-date=January 4, 2022}}</ref> and [[Timișoara]]<ref>{{cite web|url=http://www.harti-orase.ro/timisoara/strazi/strada-bolyai-janos-timisoara.html|title=Strada Bolyai János, Timișoara|lang=ro|website=www.harti-orase.ro|access-date=January 4, 2022}}</ref> are named after Bolyai.

== Gallery ==
{{Gallery
|File:Pseudosphaera2.JPG|The [[Pseudosphere]] monument in [[Târgu Mureș]]
||Statue of János Bolyai (left) and Farkas Bolyai (right) in Târgu Mureș
|File:Bolyai János-szobor.jpg|Bust of János Bolyai in [[Cluj-Napoca]]
|File:Nuseni (6).JPG|Bust of János Bolyai in [[Nușeni]]
}}

==Works==
* "Appendix scientiam spatii absolute veram exhibens; a veritate aut falsitate axiomatis XI Euclidei, a priori haud unquam", appendix to [[Farkas Bolyai]], ''Tentamen juventutem studiosam in elementa matheseos purae, elementaris ac sublimioris, methodo intuitiva, evidentiaque huic propria, introducendi (An Attempt to Introduce Studious Youths to the Elements of Pure Mathematics)'', 1832.
** English translation: [http://real-eod.mtak.hu/2790/ "The Science Absolute of Space: Independent of the Truth or Falsity of Euclid's Axiom XI (Which Can Never Be Decided A Priori)"], The Neomon, Austin, 1896.
<gallery>
File:Bolyai-1.jpg|1896 copy of Bolyai's "''The science absolute of space, independent of the truth or falsity of Euclid's axiom XI (which can never be decided a priori)''"
File:Bolyai-2.jpg|Appendix to "''The science absolute of space''"
File:Bolyai-3.jpg|First page to "''The science absolute of space''"
</gallery>

== References ==
{{Reflist|refs=
<ref name="Tóth_1965">{{cite book |title=Reguläre Figuren |chapter=1.3.4. Anmerkungen |language=de |author-first=László Fejes |author-last=Tóth |author-link=László Fejes Tóth |publisher={{ill|B. G. Teubner Verlagsgesellschaft|de|B. G. Teubner Verlag}}, Leipzig, East-Germany / [[Akadémiai Kiadó]], Budapest, Hungary |date=1965 |id=ES-No. 19 83. Kenn-No. 375. Lizenz-No. 294 |edition=1 |pages=97–98}} (2+316+6 pages, 12 [[anaglyph 3D|anaglyph]] cards, 1 red-green glasses)</ref>
}}

==Sources==
* [[Martin Gardner]] (2001) ''Non-Euclidean Geometry'', Chapter 14 of ''The Colossal Book of Mathematics'', [[W. W. Norton & Company]] {{ISBN|0-393-02023-1}}
* [[Jeremy Gray]] (2004) ''Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space,'' MIT Press {{ISBN| 0262571749}}
* [[Marvin Greenberg]] (2008) ''Euclidean and Non-Euclidean Geometries: Development and History'', 4th edition, [[W. H. Freeman and Company|W. H. Freeman]]
* Elemér Kiss (1999) ''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, {{ISBN|963-05-7563-9}};
* Tibor Weszely (2013) ''János Bolyai. Die ersten 200 Jahre'', [[Birkhäuser]], (translated from Hungarian by Manfred Stern), {{ISBN|978-3-0346-0046-0}}
* Ana Todea, Maria Fűllop, Monica Avram (2004) ''Oameni de știință mureșeni - Dicționar biobibliografic'', CJ Mureș Biblioteca Județeană Mureș, tipografia Mediaprint SRL {{in lang|ro}}
* Silva Oliva (2018) ''Janos Bolyai. Uno sguardo psicoanalitico su genio matematico e follia'', ed Mimesis.

== External links ==
* {{commons-inline}}
* {{MathGenealogy|id=101411}}
* {{cite web|url=http://telekiteka.ro/index.php?lang=en|title=The Bolyai Memorial Museum}}

{{Authority control}}

{{DEFAULTSORT:Bolyai, Janos}}
[[Category:1802 births]]
[[Category:1860 deaths]]
[[Category:Hyperbolic geometers]]
[[Category:Scientists from Cluj-Napoca]]
[[Category:Mathematicians from the Austrian Empire]]
[[Category:Transylvanian Hungarians]]
[[Category:Theresian Military Academy alumni]]
[[Category:19th-century Hungarian mathematicians]]