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Topic: Hilberts problems

	Hilberts 23 Problems
		Problem 5 - Lie's concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group.
		Problem 10 - Determination of the solvability of a diophantine equation.
		Problem 16 - Problem of the topology of algebraic curves and surfaces.
	www.cmi.ac.in /~smahanta/hilbert.html (558 words)

	David Hilbert - Wikipedia, the free encyclopedia
		Hilbert and his students supplied significant portions of the mathematical infrastructure required for quantum mechanics and general relativity.
		In an account that had become standard by the mid-century, Hilbert's problem set was also a kind of manifesto, that opened the way for the development of the formalist school, one of three major schools of mathematics of the 20th century.
		Hilbert space is the most important single idea in the area of functional analysis that grew up around it during the 20th century.
	en.wikipedia.org /wiki/David_Hilbert (2834 words)

	Hilbert's Program (Stanford Encyclopedia of Philosophy)
		He argues that whereas the intuition involved in Hilbert's early papers was a kind of perceptual intuition, in later writings (e.g., Bernays 1928a) it is identified as a form of pure intuition in the Kantian sense.
		Hilbert never gave a general account of which operations and methods of proof are acceptable from the finitist standpoint, but only examples of operations and methods of inference in contentual finitary number theory which he accepted as finitary.
		Although Hilbert's first proposals focused exclusively on consistency, there is a noticeable development in Hilbert's thinking in the direction of a general reductivist project of a sort quite common in the philosophy of science at the time (as was pointed out by Giaquinto 1983).
	plato.stanford.edu /entries/hilbert-program (7511 words)

	Hilbert's problems - Wikipedia, the free encyclopedia
		Hilbert presented ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21 and 22) at the conference, speaking on 8 August in the Sorbonne; the full list was published later.
		Hilbert was at the height of his powers and reputation at the time and would go on to lead the outstanding school of mathematics at the University of Göttingen.
		Hilbert used the function field analogy, a guide in algebraic number theory by the use of geometric analogues, in developing class field theory within his own research, and this is reflected in problem 9, to some extent in problem 12, and in problems 21 and 22.
	en.wikipedia.org /wiki/Hilbert's_problems (2568 words)

	[No title]
		Solving one of these problems is like attaining the holy grail of mathematics to some; "it would certainly include you in the honors class of the mathematical community." (1) What Hilbert accomplished with this address was as significant as any work in mathematics that he did.
		Finally Hilbert assumes that all the axioms of Euclidean geometry hold true, and the proposition that in every triangle the sum of two sides is greater than the third side is assumed as an axiom.
		The interpretation that Hilbert uses of this problem is that of Riemann.
	www.missioncollege.org /depts/math/olein.htm (1894 words)

	Hilbert's twenty-fourth problem American Mathematical Monthly, The - Find Articles (Site not responding. Last check: 2007-09-06)
		It was by the rapid publication of Hilbert's paper [37] that the importance of the problems became quite clear, and it was the American Mathematical Society that very quickly supplied English-language readers with both a report on and a translation of Hilbert's address.
		Hilbert included it neither in his address nor in any printed version, nor did he communicate it to his friends Adolf Hurwitz (1859-1919) and Hermann Minkowski (1864-1909), who were proofreaders of the paper submitted to the Gottinger Nachrichten and, more significantly, were direct participants in the developments surrounding Hilbert's ICM lecture.
		The twenty-fourth problem belongs to the realm of foundations of mathematics.
	www.findarticles.com /p/articles/mi_qa3742/is_200301/ai_n9227477 (999 words)

	Mathematical Problems by David Hilbert
		Cantor's problem of the cardinal number of the continuum.
		Problem of the straight line as the shortest distance between two points.
		Problem of the topology of algebraic curves and surfaces.
	aleph0.clarku.edu /~djoyce/hilbert/toc.html (309 words)

	Mathematical Problems of David Hilbert (Site not responding. Last check: 2007-09-06)
		Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics.
		In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century.
		Hilbert's address was more than a collection of problems.
	aleph0.clarku.edu /~djoyce/hilbert (363 words)

	Hilbert’s Problems (PRIME)
		eciding which outstanding problems in mathematics are the most important is to decide the course of mathematics’ future development.
		This problem was solved (in the affirmative) independently by Gelfond (1934) and Schneider (1935).
		This “decidability” problem is kin to the larger problem pursued by the logicist program of decidability of theories in general.
	www.mathacademy.com /pr/prime/articles/hilbert_prob (627 words)

	HONORS CLASS: HILBERT'S PROBLEMS AND THEIR SOLVERS, THE Mathematics and Computer Education - Find Articles
		Mathematicians who are able to solve the challenging problems presented by David Hubert in 1900 certainly belong in the Honors Class of mathematics.
		His presentation, along with its associated paper, provided a set of 23 clearly stated, extremely challenging problems that he expected would be solved during the 20 century.
		Yandell explains the intricacies and context of the problems, judges which of them have been solved, profiles the many mathematicians who have contributed to solving them, and provides a general history of the rest of mathematics research during the 201 century.
	www.findarticles.com /p/articles/mi_qa3950/is_200501/ai_n11826154 (618 words)

	Hilbert Tenth Problem: database index (Site not responding. Last check: 2007-09-06)
		The negative solution of this problem and the developed techniques have a lot of applications in theory of algorithms, algebra, number theory, model theory, proof theory and in theoretical computer science.
		Extensions of Hilbert's Tenth Problem (March 21 to March 25, 2005) at the American Institute of Mathematics, Palo Alto, California organized by Bjorn Poonen, Alexandra Shlapentokh, Xavier Vidaux, and Karim Zahidi.
		Conferences and meetings devoted to Hilbert's Tenth Problem and related subjects.
	logic.pdmi.ras.ru /Hilbert10 (214 words)

	[No title] (Site not responding. Last check: 2007-09-06)
		This web page highlights some of the conjectures and open problems concerning Extensions of Hilbert's Tenth Problem.
		The problem list from the workshop is available in dvi, postscript or pdf.
		Gunther Cornelissen's talk Improving Julia Robinson, along with an introduction for a general (mathematical) audience.
	www.aimath.org /WWN/hilberts10th (90 words)

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