Editing Richard Feynman (section)

== Education ==
Feynman attended [[Far Rockaway High School]], which was also attended by fellow Nobel laureates [[Burton Richter]] and [[Baruch Samuel Blumberg]].<ref>{{cite web |url=https://www.rockawave.com/articles/museum-tracks-down-frhs-nobel-laureates/ |title=Museum Tracks Down FRHS Nobel Laureates |last1=Schwach |first1=Howard |date=April 15, 2005 |publisher=The Wave |access-date=April 23, 2013 |archive-date=May 5, 2019 |archive-url=https://web.archive.org/web/20190505210032/https://www.rockawave.com/articles/museum-tracks-down-frhs-nobel-laureates/ |url-status=live}}</ref> Upon starting high school, Feynman was quickly promoted to a higher math class. An IQ test administered in high school estimated his [[Intelligence quotient|IQ]] at 125—high but "merely respectable", according to biographer [[James Gleick]].{{sfn|Gleick|1992|p=30}}{{sfn|Carroll|1996|p=9|ps=: "The general experience of psychologists in applying tests would lead them to expect that Feynman would have made a much higher IQ if he had been properly tested."}} His sister Joan, who scored one point higher, later jokingly claimed to an interviewer that she was smarter. Years later he declined to join [[Mensa International]], saying that his IQ was too low.{{sfn|Gribbin|Gribbin|1997|pp=19–20|ps=: Gleick says his IQ was 125; ''No Ordinary Genius'' says 123}}

When Feynman was 15, he taught himself [[trigonometry]], [[algebra|advanced algebra]], [[infinite series]], [[analytic geometry]], and both [[differential calculus|differential]] and [[integral calculus]].{{sfn|Schweber|1994|p=374}} Before entering college, he was experimenting with mathematical topics such as the [[half-derivative]] using his own notation.<ref>{{cite web |url=https://atomicarchive.com/resources/biographies/feynman.html |title=Richard Feynman {{pipe}} Biographies |publisher=Atomic Archive |access-date=June 10, 2023}}</ref> He created special symbols for [[logarithm]], [[sine]], [[cosine]] and [[tangent (trigonometry)|tangent]] functions so they did not look like three variables multiplied together, and for the [[derivative]], to remove the temptation of canceling out the <math>d</math>'s in <math>d/dx</math>.{{sfn|Feynman|1985|p=24}}{{sfn|Gleick|1992|p=15}} A member of the [[Arista – National Honor Society|Arista Honor Society]], in his last year in high school he won the [[New York University]] Math Championship.{{sfn|Mehra|1994|p=41}} His habit of direct characterization sometimes rattled more conventional thinkers; for example, one of his questions, when learning [[feline anatomy]], was "Do you have a map of the cat?" (referring to an anatomical chart).<!-- The book says "You mean a zoological chart!" but Feynman wanted diagrams about feline anatomy, not feline [[phylogeny]] -->{{sfn|Feynman|1985|p=72}}

Feynman applied to [[Columbia University]] but was not accepted because of its [[Jewish quota|quota for the number of Jews admitted]].<ref name="turnbull" /> Instead, he attended the [[Massachusetts Institute of Technology]], where he joined the [[Pi Lambda Phi]] fraternity.{{sfn|Gribbin|Gribbin|1997|pp=45–46}} Although he originally majored in mathematics, he later switched to electrical engineering, as he considered mathematics to be too abstract. Noticing that he "had gone too far", he then switched to physics, which he claimed was "somewhere in between".<ref>{{cite interview |last1=Feynman |first1=Richard |title=Richard Feynman – Session II |interviewer=Charles Weiner |date=March 5, 1966 |url=https://www.aip.org/history-programs/niels-bohr-library/oral-histories/5020-2 |publisher=American Institute of Physics |access-date=May 25, 2017 |archive-date=May 5, 2019 |archive-url=https://web.archive.org/web/20190505210113/https://www.aip.org/history-programs/niels-bohr-library/oral-histories/5020-2 |url-status=live}}</ref> As an undergraduate, he published two papers in the ''[[Physical Review]]''.{{sfn|Mehra|1994|p=41}} One of these, which was co-written with [[Manuel Vallarta]], was titled "The Scattering of Cosmic Rays by the Stars of a Galaxy".<ref>{{cite journal |last1=Vallarta |first1=M. S. |last2=Feynman |first2=Richard P. |date=March 1939 |title=The Scattering of Cosmic Rays by the Stars of a Galaxy |url=https://authors.library.caltech.edu/1877/1/VALpr39.pdf |url-status=live |journal=[[Physical Review]] |publisher=American Physical Society |volume=55 |issue=5 |pages=506–507 |bibcode=1939PhRv...55..506V |doi=10.1103/PhysRev.55.506.2 |archive-url=https://web.archive.org/web/20201125023157/https://authors.library.caltech.edu/1877/1/VALpr39.pdf |archive-date=November 25, 2020 |access-date=December 13, 2019| issn = 0031-899X}}</ref> {{blockquote|Vallarta let his student in on a secret of mentor-protégé publishing: the senior scientist's name comes first. Feynman had his revenge a few years later, when [[Werner Heisenberg|Heisenberg]] concluded an entire book on cosmic rays with the phrase: "such an effect is not to be expected according to Vallarta and Feynman". When they next met, Feynman asked gleefully whether Vallarta had seen Heisenberg's book. Vallarta knew why Feynman was grinning. "Yes," he replied. "You're the last word in cosmic rays."{{sfn|Gleick|1992|p=82}}}}

The other was his senior thesis, on "Forces in Molecules",<ref>{{cite journal |title=Forces in Molecules |url=https://authors.library.caltech.edu/3515/ |last=Feynman |first=R. P. |journal=Physical Review |volume=56 |issue=4 |pages=340–343 |date=August 1939 |publisher=American Physical Society |doi=10.1103/PhysRev.56.340 |bibcode=1939PhRv...56..340F |s2cid=121972425 |access-date=May 20, 2019 |archive-date=September 19, 2020 |archive-url=https://web.archive.org/web/20200919050513/https://authors.library.caltech.edu/3515/ |url-status=live}}</ref> based on a topic assigned by [[John C. Slater]], who was sufficiently impressed by the paper to have it published. Its main result is known as the [[Hellmann–Feynman theorem]].{{sfn|Mehra|1994|pp=71–78}}

In 1939, Feynman received a [[bachelor's degree]]{{sfn|Gribbin|Gribbin|1997|p=56}} and was named a [[Putnam Fellow]].<ref name=MMA>{{cite web |title=List of Previous Putnam Winners |url=https://www.maa.org/sites/default/files/pdf/Putnam/Competition_Archive/List%20of%20Previous%20Putnam%20Winners.pdf |publisher=Mathematical Association of America |access-date=June 10, 2023}}</ref> He attained a perfect score on the graduate school entrance exams to [[Princeton University]] in physics—an unprecedented feat—and an outstanding score in mathematics, but did poorly on the history and English portions. The head of the physics department there, [[Henry D. Smyth]], had another concern, writing to [[Philip M. Morse]] to ask: "Is Feynman Jewish? We have no definite rule against Jews but have to keep their proportion in our department reasonably small because of the difficulty of placing them."{{sfn|Gleick|1992|p=84}} Morse conceded that Feynman was indeed Jewish, but reassured Smyth that Feynman's "physiognomy and manner, however, show no trace of this characteristic".{{sfn|Gleick|1992|p=84}}

Attendees at Feynman's first seminar, which was on the classical version of the [[Wheeler–Feynman absorber theory]], included [[Albert Einstein]], [[Wolfgang Pauli]], and [[John von Neumann]]. Pauli made the prescient comment that the theory would be extremely difficult to quantize, and Einstein said that one might try to apply this method to gravity in [[general relativity]],{{sfn|Feynman|1985|pp=77–80}} which [[Sir Fred Hoyle]] and [[Jayant Narlikar]] did much later as the [[Hoyle–Narlikar theory of gravity]].<ref>{{cite magazine |url=http://www.time.com/time/magazine/article/0,9171,898186,00.html |archive-url=https://web.archive.org/web/20111213230334/http://www.time.com/time/magazine/article/0,9171,898186,00.html |url-status=dead |archive-date=December 13, 2011 |title=Cosmology: Math Plus Mach Equals Far-Out Gravity |date=June 26, 1964 |magazine=Time |access-date=August 7, 2010}}</ref><ref>{{cite journal |last1=Hoyle |first1=F. |last2=Narlikar |first2=J. V. |date=1964 |title=A New Theory of Gravitation |journal=[[Proceedings of the Royal Society A]] |volume=282 |issue=1389 |pages=191–207 |bibcode=1964RSPSA.282..191H |doi=10.1098/rspa.1964.0227 |s2cid=59402270}}</ref> Feynman received a PhD from Princeton in 1942; his thesis advisor was [[John Archibald Wheeler]].{{sfn|Gleick|1992|pp=129–130}} In his doctoral thesis titled "The Principle of Least Action in Quantum Mechanics",<ref>{{cite thesis |title=The Principle of Least Action in Quantum Mechanics |url=https://cds.cern.ch/record/101498/files/Thesis-1942-Feynman.pdf |access-date=July 12, 2016 |type=PhD |publisher=Princeton University |year=1942 |first=Richard P. |last=Feynman |archive-date=December 20, 2019 |archive-url=https://web.archive.org/web/20191220132015/https://cds.cern.ch/record/101498/files/Thesis-1942-Feynman.pdf |url-status=live}}</ref> Feynman applied the [[principle of stationary action]] to problems of quantum mechanics, inspired by a desire to quantize the Wheeler–Feynman absorber theory of electrodynamics, and laid the groundwork for the path integral formulation and Feynman diagrams.{{sfn|Mehra|1994|pp=92–101}} A key insight was that [[positron]]s behaved like [[electron]]s moving backwards in time.{{sfn|Mehra|1994|pp=92–101}} James Gleick wrote:
{{blockquote|This was Richard Feynman nearing the crest of his powers. At twenty-three&nbsp;... there may now have been no physicist on earth who could match his exuberant command over the native materials of theoretical science. It was not just a facility at mathematics (though it had become clear&nbsp;... that the mathematical machinery emerging in the Wheeler–Feynman collaboration was beyond Wheeler's own ability). Feynman seemed to possess a frightening ease with the substance behind the equations, like Einstein at the same age, like the Soviet physicist [[Lev Landau]]—but few others.{{sfn|Gleick|1992|pp=129–130}} |sign=|source=}}

One of the conditions of Feynman's scholarship to Princeton was that he could not be married; nevertheless, he continued to see his high school sweetheart, Arline Greenbaum, and was determined to marry her once he had been awarded his PhD despite the knowledge that she was seriously ill with [[tuberculosis]]. This was an incurable disease at the time, and she was not expected to live more than two years. On June 29, 1942, they took the [[Staten Island Ferry|ferry]] to [[Staten Island]], where they were married in the city office. The ceremony was attended by neither family nor friends and was witnessed by a pair of strangers. Feynman could kiss Arline only on the cheek. After the ceremony he took her to [[Deborah Heart and Lung Center|Deborah Hospital]], where he visited her on weekends.{{sfn|Gribbin|Gribbin|1997|pp=66–67}}{{sfn|Gleick|1992|pp=150–151}}