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Topic: Foundations problem in mathematics

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	Foundations problem in mathematics Article, Foundationsproblemmathematics Information (Site not responding. Last check: 2007-10-09)
		The foundations problem in mathematics was the late 19thcentury and early 20th century term for the search for the simplest metamathematics.
		Today one refers more ambiguously to the foundations of mathematics to avoid giving the impression that there is a 'problem' that can besolved in the sense of a science or mathematics problem, with a single right answer that is checked by means describable in proof theory.
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	www.anoca.org /assumption/term/foundations_problem_in_mathematics.html (257 words)

	Foundations of mathematics (Site not responding. Last check: 2007-10-09)
		Thomists and Thomas Aquinas on the foundation of mathematics.
		The term "foundations of mathematics" is sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory.
		Some theories tend to focus on mathematical practice, and aim to describe and analyze the actual working of mathematicians as a social group.
	hallencyclopedia.com /Foundations_of_mathematics (732 words)

	ipedia.com: Foundations problem in mathematics Article (Site not responding. Last check: 2007-10-09)
		After several schools of the philosophy of mathematics met limitations one after the other in the 20th century, the assumption that any foundation could be successfully modelled within mathematics itself began to be heavily challenged.
		Today one refers more ambiguously to the foundations of mathematics to avoid giving the impression that there is a 'problem' that can be solved in the sense of a science or mathematics problem, with a single right answer that is checked by means describable in proof theory.
		The term 'foundations problem' only occurs in literature that makes the assumption that there is such a provable and single foundation.
	www.ipedia.com /foundations_problem_in_mathematics.html (235 words)

	Foundations of Mathematics
		The Theory of The Foundations of Mathematics - 1870 to 1940 - by Mark Scheffer
		The Foundations of Mathematics: A Contribution to The Philosophy of Geometry - by Paul Carus
		Andrey Markov - from Laboratory of Mathematical Logic of Steklov Institute of Mathematics at St.Petersburg
	sakharov.net /foundation_rt.html (2708 words)

	On Computable Numbers, with an Application to the Entscheidungsproblem [Decision Problem] [encyclopedia] (Site not responding. Last check: 2007-10-09)
		Turing showed that the machine in principle was able to do all mathematical operations and that there was no general way to determine if a computation would ever stop.
		From this he concluded that it is not possible to determine if a theorem is provable or not without actually finding the proof.
		You can also informally appreciate the halting problem by considering the consequences of having a subroutine, e.g.
	kosmoi.com /Computer/Science/Entscheidungsproblem (1128 words)

	Mathematics - Foundations Of Mathematics (Site not responding. Last check: 2007-10-09)
		From The Mathematical Atlas, a resource of mathematics maintained by David Rusin.
		Institute for the History and Foundations of Science, based in the Netherlands.
		Institute for Mathematical Logic and Foundations of Mathematics.
	mathematics.information-about.net /foundationsofmathematics (144 words)

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