Edward Nelson
Edward Nelson | |
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Born | |
Died | September 10, 2014 | (aged 82)
Citizenship | American |
Alma mater |
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Known for | |
Spouses |
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Children | 2 |
Awards | |
Scientific career | |
Fields | |
Institutions | |
Thesis | On the Operator Theory of Markoff Processes |
Doctoral advisor | Irving Segal |
Notable students |
Edward Nelson(May 4, 1932 – September 10, 2014) was an American mathematician. He was professor in the Mathematics Department atPrinceton University.He was known for his work onmathematical physicsandmathematical logic.In mathematical logic, he was noted especially for hisinternal set theory,and views onultrafinitismand theconsistencyofarithmetic.Inphilosophy of mathematicshe advocated the view offormalismrather thanplatonismorintuitionism.He also wrote on the relationship between religion and mathematics.[1][2][3]
Biography
[edit]Edward Nelson was born inDecatur, Georgia,in 1932. He spent his early childhood inRomewhere his father worked for the Italian YMCA. At the advent ofWorld War II,Nelson moved with his mother toNew York City,where he attended high school at theBronx High School of Science.His father, who spoke fluentRussian,stayed inSt. Petersburgin connection with issues related toprisoners of war.After the war, his family returned to Italy and he attended theLiceo ScientificoGiovanni Verga in Rome.[4]
He received his Ph.D. in 1955 from theUniversity of Chicago,where he worked withIrving Segal.He was a member of theInstitute for Advanced Studyfrom 1956 to 1959. He held a position atPrinceton Universitystarting in 1959, attaining the rank of professor there in 1964 and retiring in 2013.
In 2012 he became a fellow of theAmerican Mathematical Society.[5]He died inPrinceton, New Jersey,on September 10, 2014.[6]
Academic work
[edit]Stochastic quantum mechanics
[edit]Nelson made contributions to the theory of infinite-dimensionalgroup representations,the mathematical treatment ofquantum field theory,the use ofstochastic processesinquantum mechanics,and the reformulation ofprobability theoryin terms ofnon-standard analysis.For many years he worked onmathematical physicsand probability theory, and he retained a residual interest in these fields, particularly in connection with possible extensions of stochastic mechanics tofield theory.
Four color problem
[edit]In 1950, Nelson formulated a popular variant of thefour color problem:What is the chromatic number, denoted,of the plane? In more detail, what is the smallest number of colors sufficient for coloring the points of the Euclidean plane such that no two points of the same color are unit distance apart?[7]We know by simple arguments that 4 ≤χ≤ 7. The problem was introduced to a wide mathematical audience byMartin Gardnerin his October 1960Mathematical Gamescolumn. The chromatic number problem, also now known as theHadwiger–Nelson problem,was a favorite ofPaul Erdős,who mentioned it frequently in his problems lectures. In 2018,Aubrey de Greyshowed thatχ≥ 5.[8]
Foundations of mathematics
[edit]In the later part of his career, he worked on mathematical logic and the foundations of mathematics. One of his goals was to extend IST (Internal Set Theory—a version of a portion ofAbraham Robinson'snon-standard analysis) in a natural manner that includes external functions and sets, in a way that provides an external function with specified properties unless there is a finitary obstacle to its existence. Other work centered on fragments of arithmetic, studying the divide between those theories interpretable inRaphael Robinson's arithmeticand those that are not;computational complexity,including the problem of whetherP is equal to NP or not;andautomated proof checking.
In September 2011, Nelson announced that he had proved thatPeano arithmeticwas logically inconsistent.[9]An error was found in the proof byTerence Tao,and Nelson retracted the claim.[10]
Publications
[edit]Selected papers
[edit]- Nelson, Edward (1966)."Derivation of the Schrödinger Equation from Newtonian Mechanics"(PDF).Physical Review.150(4): 1079–1085.Bibcode:1966PhRv..150.1079N.doi:10.1103/PhysRev.150.1079.ISSN0031-899X.
- Nelson, E. (1986). "Field Theory and the Future of Stochastic Mechanics". In Albeverio, S.; Casati, G.; Merlini, D. (eds.).Stochastic Processes in Classical and Quantum Systems.Lecture Notes in Physics. Vol. 262. Berlin: Springer-Verlag. pp. 438–469.doi:10.1007/3-540-17166-5.ISBN978-3-662-13589-1.OCLC864657129.
Books
[edit]- Nelson, E. (1967).Dynamical theories of Brownian Motion.Princeton: Princeton University Press.ISBN978-0-691-07950-9.OCLC769464.
- Nelson, E. (1967).Tensor Analysis.Princeton: Princeton University Press.ISBN9781400879236.LCCN67028943.OCLC988417.
- Nelson, E. (1969).Topics in Dynamics: I: Flows.Princeton: Princeton University Press.ISBN0-691-08080-1.LCCN79108265.OCLC59197.
- Nelson, E. (1985).Quantum Fluctuations.Princeton: Princeton University Press.ISBN0-691-08378-9.LCCN84026449.OCLC11549759.
- Nelson, E. (1986).Predicative Arithmetic.Princeton: Princeton University Press.ISBN0-691-08455-6.LCCN86018730.OCLC14001745.[11]
- Nelson, E. (1987).Radically Elementary Probability Theory.Princeton: Princeton University Press.ISBN0-691-08473-4.LCCN87003160.OCLC15591889.
See also
[edit]References
[edit]Notes
[edit]- ^Edward Nelson (2000)."Mathematics and Faith"(PDF).Presented at the Jubilee for Men and Women from the World of Learning, held at the Vatican, 23–24 May 2000.RetrievedMarch 5,2020.
{{cite web}}
:CS1 maint: location (link) - ^Edward Nelson (2009)."Completed Infinity and Religion".RetrievedMarch 5,2020.
- ^
Nelson, Edward (October 17, 2009).Mathematics and Religion(Speech). The Philoctetes Center for the Multidisciplinary Study of the Imagination. 31 minutes in.
In terms of religion, I'm a Christian. Worship and prayer are very important to me.
- ^Aizenman, Michael; Kochen, Simon; Lieb, Elliott; Simon, Barry; Gunning, Robert (2014)."Edward Nelson 1932-2014".Princeton University Department of Mathematics.The Trustees of Princeton University.RetrievedMarch 5,2021.
- ^AMS 2012.
- ^Princeton University 2014.
- ^Soifer 2009,p. 23.
- ^de Grey, Aubrey D.N.J. (2018), "The Chromatic Number of the Plane Is at least 5",Geombinatorics,28:5–18,arXiv:1804.02385,Bibcode:2016arXiv160407134W.
- ^Nelson 2011.
- ^Baez 2011.
- ^Wilkie 1990.
Sources
[edit]- American Mathematical Society(2012)."List of Fellows of the American Mathematical Society".ams.org.American Mathematical Society. Archived fromthe originalon December 5, 2012.
- Baez, J.(2011)."The Inconsistency of Arithmetic".golem.ph.utexas.edu.The n-Category Café.
- Katz, M. G.;Kutateladze, Semen S.(2015). "Edward Nelson (1932–2014)".The Review of Symbolic Logic.8(3): 607–610.arXiv:1506.01570.Bibcode:2015arXiv150601570K.doi:10.1017/S1755020315000015.ISSN1755-0203.S2CID42672640.
- Kelly, M. (2014)."Edward Nelson, Nonconformist who Sparked a Quantum Field Theory Revolution, Dies at 82".princeton.edu.Princeton University. Archived fromthe originalon June 7, 2017.
- Nelson, E. (2011)."Inconsistency of P".cs.nyu.edu.Foundations of Mathematics. Archived fromthe originalon May 13, 2017.
- Princeton University(2014)."Professor Emeritus Edward Nelson Passed Away September 10th".math.princeton.edu.Archived fromthe originalon September 11, 2014.
{{cite web}}
:CS1 maint: ref duplicates default (link) - Soifer, A.(2009).The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators.New York: Springer.ISBN978-0-387-74640-1.LCCN2008936132.OCLC233933503.
- Wilkie, A. J.(1990)."Book Review: Predicative Arithmetic"(PDF).Bulletin of the American Mathematical Society.22(2): 326–332.doi:10.1090/S0273-0979-1990-15900-2.ISSN0273-0979.
External links
[edit]- 1932 births
- Members of the United States National Academy of Sciences
- Fellows of the American Mathematical Society
- 20th-century American mathematicians
- 21st-century American mathematicians
- American logicians
- Set theorists
- University of Chicago alumni
- Princeton University faculty
- 2014 deaths
- American mathematical physicists