Edward Nelson

Edward Nelson
Edward Nelson
	Edward Nelson
Born	May 4, 1932; Decatur, Georgia
Died	September 10, 2014(aged 82); Princeton, New Jersey
Citizenship	American
Alma mater	University of Chicago(MS, 1953); University of Chicago(PhD, 1955);
Known for	Internal set theory; Stochastic quantum mechanics; Stochastic quantization; Hadwiger–Nelson problem; Nelson's axioms;
Spouses	Nancy Wong Nelson; Sarah Jones Nelson;
Children	2
Awards	Leroy P. Steele Prize;
	Scientific career
Fields	Physics; Mathematics;
Institutions	Institute for Advanced Study; Princeton University;
Thesis	On the Operator Theory of Markoff Processes
Doctoral advisor	Irving Segal
Notable students	Eric Anders Carlen; Richard M. Dudley; John D. Lafferty; Greg Lawler;

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

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

Stochastic quantum mechanics

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

In 1950, Nelson formulated a popular variant of thefour color problem:What is the chromatic number, denoted $\chi$ ,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

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

Selected papers

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.ISSN 0031-899X.
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.ISBN 978-3-662-13589-1.OCLC 864657129.

Books

Nelson, E. (1967).Dynamical theories of Brownian Motion.Princeton: Princeton University Press.ISBN 978-0-691-07950-9.OCLC 769464.
Nelson, E. (1967).Tensor Analysis.Princeton: Princeton University Press.ISBN 9781400879236.LCCN 67028943.OCLC 988417.
Nelson, E. (1969).Topics in Dynamics: I: Flows.Princeton: Princeton University Press.ISBN 0-691-08080-1.LCCN 79108265.OCLC 59197.
Nelson, E. (1985).Quantum Fluctuations.Princeton: Princeton University Press.ISBN 0-691-08378-9.LCCN 84026449.OCLC 11549759.
Nelson, E. (1986).Predicative Arithmetic.Princeton: Princeton University Press.ISBN 0-691-08455-6.LCCN 86018730.OCLC 14001745.^[11]
Nelson, E. (1987).Radically Elementary Probability Theory.Princeton: Princeton University Press.ISBN 0-691-08473-4.LCCN 87003160.OCLC 15591889.

References

Notes

^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

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.ISSN 1755-0203.S2CID 42672640.
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.ISBN 978-0-387-74640-1.LCCN 2008936132.OCLC 233933503.
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.ISSN 0273-0979.

External links

[1] 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)

[2] Edward Nelson (2009)."Completed Infinity and Religion".RetrievedMarch 5,2020.

[3] 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.

[4] 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.

[FOOTNOTEAMS2012-5] AMS 2012.

[FOOTNOTEPrinceton_University2014-6] Princeton University 2014.

[FOOTNOTESoifer200923-7] Soifer 2009,p. 23.

[8] 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.

[FOOTNOTENelson2011-9] Nelson 2011.

[FOOTNOTEBaez2011-10] Baez 2011.

[FOOTNOTEWilkie1990-11] Wilkie 1990.

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