Editing John von Neumann (section)

=== 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}}