Editing John von Neumann (section)

== Life and education ==
=== Family background ===
Von Neumann was born in [[Budapest]], Kingdom of Hungary (then part of Austria-Hungary),<ref>{{cite book |editor-last1=Doran |editor-first1=Robert S. |editor-link1=Robert S. Doran |editor-link2=Richard Kadison |editor-first2=Richard V. |editor-last2=Kadison |title=Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration Honoring John von Neumann and Marshall H. Stone |publisher=American Mathematical Society |location=Washington, D.C. |year=2004 |url=https://bookstore.ams.org/conm-365 |isbn=978-0-8218-3402-2 |page=1}}</ref><ref name= Time>{{cite news |last=Myhrvold |first=Nathan |author-link=Nathan Myhrvold |date=March 21, 1999 |url=http://www.time.com/time/magazine/article/0,9171,21839,00.html |archive-url=https://web.archive.org/web/20010211124237/http://www.time.com/time/magazine/article/0,9171,21839,00.html |url-status=dead |archive-date=February 11, 2001 |title=John von Neumann |newspaper=[[Time (magazine)|Time]]}}</ref>{{sfn|Blair|1957|p=104}} on December 28, 1903, to a wealthy, non-observant [[Jewish]] family. His birth name was '''Neumann János Lajos'''. In Hungarian, the family name comes first, and his given names are equivalent to John Louis in English.{{sfn|Bhattacharya|2022|p=4}}

He was the eldest of three brothers; his two younger siblings were Mihály (Michael) and Miklós (Nicholas).{{sfn|Dyson|1998|p=xxi}} His father Neumann Miksa (Max von Neumann) was a banker and held a [[doctor of law|doctorate in law]]. He had moved to Budapest from [[Pécs]] at the end of the 1880s.{{sfn|Macrae|1992|pp=38–42}} Miksa's father and grandfather were born in Ond (now part of [[Szerencs]]), [[Zemplén County]], northern Hungary. John's mother was Kann Margit (Margaret Kann);{{sfn|Macrae|1992|pp=37–38}} her parents were Kann Jákab and Meisels Katalin of the [[Meisel family|Meisels family]].{{sfn|Macrae|1992|p=39}} Three generations of the Kann family lived in spacious apartments above the Kann-Heller offices in Budapest; von Neumann's family occupied an 18-room apartment on the top floor.{{sfn|Macrae|1992|pp=44–45}}

On February 20, 1913, [[Emperor Franz Joseph]] elevated John's father to the Hungarian nobility for his service to the Austro-Hungarian Empire.<ref name="archives.hungaricana.hu">{{cite web
|title       = Neumann de Margitta Miksa a Magyar Jelzálog-Hitelbank igazgatója n:Kann Margit gy:János-Lajos, Mihály-József, Miklós-Ágost {{!}} Libri Regii {{!}} Hungaricana
|url         = https://archives.hungaricana.hu/en/libriregii/hu_mnl_ol_a057_72_1096/?list=eyJxdWVyeSI6ICJuZXVtYW5uIn0
|access-date = 2022-08-08
|website     = archives.hungaricana.hu
|language    = Hungarian
}}</ref> The Neumann family thus acquired the hereditary appellation ''Margittai'', meaning "of Margitta" (today [[Marghita]], Romania). The family had no connection with the town; the appellation was chosen in reference to Margaret, as was their chosen [[coat of arms]] depicting three [[Argyranthemum|marguerites]]. Neumann János became margittai Neumann János (John Neumann de Margitta), which he later changed to the German Johann von Neumann.{{sfn|Macrae|1992|pp=57–58}}

=== Child prodigy ===
Von Neumann was a [[child prodigy]] who at six years old could divide two eight-digit numbers in his head<ref>{{cite book |last=Henderson |first=Harry |title=Mathematics: Powerful Patterns Into Nature and Society |publisher=Chelsea House |location=New York |year=2007 |isbn=978-0-8160-5750-4|oclc=840438801 |page=30 }}</ref>{{sfn|Schneider|Gersting|Brinkman|2015|p=28}} and converse in [[Ancient Greek]].<ref>{{cite book |last=Mitchell |first=Melanie |author-link=Melanie Mitchell |title=Complexity: A Guided Tour |publisher=Oxford University Press |year=2009 |isbn=978-0-19-512441-5 |oclc=216938473 |page=124}}</ref> He, his brothers and his cousins were instructed by governesses. Von Neumann's father believed that knowledge of languages other than their native [[Hungarian language|Hungarian]] was essential, so the children were tutored in [[English (language)|English]], [[French (language)|French]], [[German (language)|German]] and [[Italian (language)|Italian]].{{sfn|Macrae|1992|pp=46–47}} By age eight, von Neumann was familiar with [[differential calculus|differential]] and [[integral calculus]], and by twelve he had read [[Émile Borel|Borel's]] ''La Théorie des Fonctions''.{{sfn|Halmos|1973|p=383}} He was also interested in history, reading [[Wilhelm Oncken]]'s 46-volume world history series {{lang|de|Allgemeine Geschichte in Einzeldarstellungen}} (''General History in Monographs'').{{sfn|Blair|1957|p=90}} One of the rooms in the apartment was converted into a library and reading room.{{sfn|Macrae|1992|p=52}}

Von Neumann entered the Lutheran [[Fasori Gimnázium|Fasori Evangélikus Gimnázium]] in 1914.{{sfn|Aspray|1990}} [[Eugene Wigner]] was a year ahead of von Neumann at the school and soon became his friend.{{sfn |Macrae |1992 |pp=70–71}}

Although von Neumann's father insisted that he attend school at the grade level appropriate to his age, he agreed to hire private tutors to give von Neumann advanced instruction. At 15, he began to study advanced calculus under the analyst [[Gábor Szegő]].{{sfn|Macrae|1992|pp=70–71}} On their first meeting, Szegő was so astounded by von Neumann's mathematical talent and speed that, as recalled by his wife, he came back home with tears in his eyes.<ref>Impagliazzo, John; [[James Glimm|Glimm, James]]; [[Isadore Singer|Singer, Isadore Manuel]] [https://books.google.com/books?id=XBK-r0gS0YMC&pg=PA15 ''The Legacy of John von Neumann''], American Mathematical Society, 1990, p. 5, {{ISBN|0-8218-4219-6}}.</ref> By 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of [[ordinal number#Von Neumann definition of ordinals|ordinal numbers]], which superseded [[Georg Cantor]]'s definition.<ref name=Nasar-p81>{{cite book |last=Nasar |first=Sylvia |author-link=Sylvia Nasar |year=2001 |title=A Beautiful Mind : a Biography of John Forbes Nash, Jr., Winner of the Nobel Prize in Economics, 1994 |location=London |publisher=Simon & Schuster |isbn=978-0-7432-2457-4  |url=https://archive.org/details/beautifulmindli00nasa |page=81}}</ref> At the conclusion of his education at the gymnasium, he applied for and won the Eötvös Prize, a national award for mathematics.{{sfn|Macrae|1992|p=84}}

=== University studies ===
According to his friend [[Theodore von Kármán]], von Neumann's father wanted John to follow him into industry, and asked von Kármán to persuade his son not to take mathematics.<ref>von Kármán, T., & Edson, L. (1967). The wind and beyond. Little, Brown & Company.</ref> Von Neumann and his father decided that the best career path was [[chemical engineer]]ing. This was not something that von Neumann had much knowledge of, so it was arranged for him to take a two-year, non-degree course in chemistry at the [[University of Berlin]], after which he sat for the entrance exam to [[ETH Zurich]],{{sfn|Macrae|1992|pp=85–87}} which he passed in September 1923.{{sfn|Macrae|1992|p=97}} Simultaneously von Neumann entered [[Eötvös Loránd University|Pázmány Péter University]], then known as the University of Budapest, as a [[Doctor of Philosophy|Ph.D.]] candidate in [[mathematics]].<ref name="NYT">{{cite news |last=Regis |first=Ed |author-link=Ed Regis (author) |title=Johnny Jiggles the Planet |url=https://query.nytimes.com/gst/fullpage.html?res=9E0CE7D91239F93BA35752C1A964958260 |work=The New York Times |date=November 8, 1992 |access-date=2008-02-04}}</ref> For his thesis, he produced an [[axiomatization]] of [[Georg Cantor#Set theory|Cantor's set theory]].<ref name="Neumann1928">{{cite journal|last1=von Neumann|first1=J. |title=Die Axiomatisierung der Mengenlehre|journal=Mathematische Zeitschrift|volume=27|issue=1|year=1928|pages=669–752|issn=0025-5874|doi=10.1007/BF01171122|s2cid=123492324 |language=de}}</ref>{{sfn|Macrae|1992|pp=86–87}} In 1926, he graduated as a [[chemical engineer]] from ETH Zurich and simultaneously passed his final examinations ''[[summa cum laude]]'' for his Ph.D. in mathematics (with minors in [[experimental physics]] and chemistry) at the University of Budapest.<ref>{{cite book |last1=Wigner |first1=Eugene |author-link=Eugene Wigner |year=2001 |chapter=John von Neumann (1903–1957) |editor-last1=Mehra |editor-first1=Jagdish |editor-link=Jagdish Mehra |title=The Collected Works of Eugene Paul Wigner: Historical, Philosophical, and Socio-Political Papers. Historical and Biographical Reflections and Syntheses |publisher=Springer |location=Berlin |doi=10.1007/978-3-662-07791-7 |isbn=978-3-662-07791-7 |page=128}}</ref>{{sfn|Pais|2000|p=187}}

He then went to the [[University of Göttingen]] on a grant from the [[Rockefeller Foundation]] to study mathematics under [[David Hilbert]].{{sfn|Macrae|1992|pp=98–99}} [[Hermann Weyl]] remembers how in the winter of 1926–1927 von Neumann, [[Emmy Noether]], and he would walk through "the cold, wet, rain-wet streets of [[Göttingen]]" after class discussing [[hypercomplex number]] systems and their [[Representation theory|representations]].<ref>{{cite book |last1=Weyl |first1=Hermann |editor1-last=Pesic |editor1-first=Peter |title=Levels of Infinity: Selected Writings on Mathematics and Philosophy |date=2012 |publisher=Dover Publications |isbn=978-0-486-48903-2 |page=55 |edition=1}}</ref>