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Applications with CSG support: Clara.io supports CSG booleans.

← Older revision		Revision as of 16:05, 31 January 2014
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			{{BLP sources\|date=February 2013}}
			'''Edward Nelson''' (born May 4, 1932, in [[Decatur, Georgia]]) is a professor in the Mathematics Department at [[Princeton University]]. He is known for his work on [[mathematical physics]] and [[mathematical logic]]. In mathematical logic, he is noted especially for his [[internal set theory]], and his controversial views on [[ultrafinitism]] and the [[consistency]] of [[Peano arithmetic\|arithmetic]]. He has also written on the relationship between religion and mathematics.

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			Nelson received his Ph.D. in 1955 from the [[University of Chicago]], where he worked with [[Irving Segal]]. He was a member of the [[Institute for Advanced Study]] from 1956–1959. He has held a position at [[Princeton University]] from 1959 to the present, attaining the rank of professor there in 1964.

			In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-02-24.</ref>

			==Early work==

			Nelson has made contributions to the theory of infinite dimensional [[group representation]]s, the mathematical treatment of [[quantum field theory]], the use of [[stochastic process]]es in [[quantum mechanics]], and the reformulation of [[probability theory]] in terms of [[non-standard analysis]].

			For many years he worked on [[mathematical physics]] and probability theory, and still has a residual interest in these fields, particularly in possible extensions of stochastic mechanics to [[field theory (physics)\|field theory]].

			In 1950, Nelson formulated a popular variant of the [[four color problem]]. What is the chromatic number, denoted <math>\chi</math>, of the plane? In more detail, what is the smallest number of colors sufficient for coloring the points of the Euclidean plane in such a way that no two points of the same color are unit distance apart?<ref>p.23, Soifer, Alexander (2008); The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators; New York: Springer. ISBN 978-0-387-74640-1</ref> We know by simple arguments that 4 ≤ ''χ'' ≤ 7. The problem was introduced to a wide mathematical audience by [[Martin Gardner]] in his October 1960 [[Mathematical Games]] column. The chromatic number problem, also now known as the [[Hadwiger–Nelson problem]], was also a favorite of [[Paul Erdős]], who mentioned it frequently in his problems lectures.

			==Work on foundations==
			In recent years he has been working on mathematical logic and the foundations of mathematics. One of his goals is to extend IST ([[Internal Set Theory]]—a version of a portion of [[Abraham Robinson]]'s [[non-standard analysis]]) in a natural way to include 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 centers on fragments of arithmetic, studying the divide between those theories interpretable in [[Robinson arithmetic\|Raphael Robinson's Arithmetic]] and those that are not; [[computational complexity theory\|computational complexity]], including the problem of whether [[P = NP problem\|P is equal to NP or not]]; and automated proof checking.

			In September 2011, Nelson announced that he had proved that [[Peano arithmetic]] was logically inconsistent. An error was found in the proof, and he retracted the claim.

			==Publications==
			*''Dynamical theory of Brownian motion.'' Princeton University Press 1967
			*''Topics in Dynamics 1: Flows.'' Princeton University Press 1969
			*''Tensor analysis.'' Princeton University Press 1967
			*''Quantum Fluctuations.'' Princeton University Press, 1985
			*''Predicative Arithmetic.'' Princeton University Press, 1986<ref>{{cite journal\|author=Wilkie, A. J.\|authorlink=Alex Wilkie\|title=Review: ''Predicative arithmetic'', by Edward Nelson\|journal=Bull. Amer. Math. Soc. (N.S.)\|year=1990\|volume=22\|issue=2\|pages=326–331\|url=http://www.ams.org/journals/bull/1990-22-02/S0273-0979-1990-15900-2/}}</ref>
			*''Radically elementary probability theory.'' Annals of Mathematical Studies, Princeton 1987

			==Notes==
			{{reflist}}

			==See also==
			*[[Influence of non-standard analysis]]

			==References==
			* [http://math.princeton.edu/~nelson/cv.pdf Curriculum Vitae]
			* [https://web.math.princeton.edu/~nelson/papers/faith.pdf Mathematics and Faith (PDF)]

			==External links==
			*[http://www.math.princeton.edu/~nelson/ Edward Nelson's Homepage]

			{{Authority control\|VIAF=108601931}}

			{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
			\| NAME = Nelson, Edward
			\| ALTERNATIVE NAMES =
			\| SHORT DESCRIPTION = American mathematician
			\| DATE OF BIRTH = May 4, 1932
			\| PLACE OF BIRTH =
			\| DATE OF DEATH =
			\| PLACE OF DEATH =
			}}
			{{DEFAULTSORT:Nelson, Edward}}
			[[Category:1932 births]]
			[[Category:Members of the United States National Academy of Sciences]]
			[[Category:Fellows of the American Mathematical Society]]
			[[Category:American Christians]]
			[[Category:American mathematicians]]
			[[Category:American logicians]]
			[[Category:Set theorists]]
			[[Category:University of Chicago alumni]]
			[[Category:Princeton University faculty]]
			[[Category:Living people]]
			[[Category:Mathematical physicists]]
			[[Category:American philosophers]]

89.180.54.137: /* Applications with CSG support */ Added GiDES++ application

2012-08-31T15:44:05Z

Applications with CSG support: Added GiDES++ application

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