
	Where results make sense

Topic: Mathematical rigour

In the News (Tue 29 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Rigour - Wikipedia, the free encyclopedia
		Mathematical rigour is often cited as a kind of gold standard for mathematical proof.
		Complete rigour, it is often said, became available in mathematics at the start of the twentieth century.
		Most mathematical arguments are presented as prototypes of formally rigorous proofs, on the grounds that too much formality may in fact obscure what is being demonstrated.
	en.wikipedia.org /wiki/Rigour (658 words)

	Mathematics - Wikipedia, the free encyclopedia
		Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.
		Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not utilize the Scientific Method.
		Mathematical logic is concerned with setting mathematics on a rigid axiomatic framework, and studying the results of such a framework.
	en.wikipedia.org /wiki/Mathematics (3880 words)

	Mathematical physics - Wikipedia, the free encyclopedia
		Mathematical physics is the scientific discipline concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories"
		Revolutionary mathematical physicists at the turn of the 20th century included the mathematician David Hilbert who devised the theory of Hilbert spaces for integral equations which would find a major application in quantum mechanics.
		The term 'mathematical' physics is also sometimes used in a special sense, to distinguish research aimed at studying and solving problems inspired by physics within a mathematically rigorous framework.
	en.wikipedia.org /wiki/Mathematical_Physics (660 words)

	Rigour - Biocrawler (Site not responding. Last check: 2007-10-24)
		Rigour (American English: "rigor") has a number of meanings in relation to intellectual life and discourse.
		It has a history, being traced back to Greek mathematics, where it is said to have been invented.
		Most mathematical arguments are presented as prototypes of formally rigorous proofs, on the grounds that too much formality may in fact obscure what is being said.
	www.biocrawler.com /encyclopedia/Rigor (657 words)

	ScienceDaily: Mathematics (Site not responding. Last check: 2007-10-24)
		Mathematics is often defined as the study of topics such as quantity, structure, space, and change.
		Mathematics, in nearly every society, is used in fields such as the natural sciences, engineering, measuring land, predicting astronomical events, medicine, accounting, and economics.
		Mathematics -- Mathematics is often defined as the study of topics such as quantity, structure, space, and change.
	www.sciencedaily.com /encyclopedia/mathematics (4202 words)

	Mathematics - Facts, Information, and Encyclopedia Reference article
		Mathematics is often defined as the study of certain topics, such as quantity, structure, space, and change.
		Nowadays, mathematics derives much inspiration from the natural sciences and it is not uncommon for new mathematics to be pioneered by physicists, although it may need to be recast into more rigorous language.
		Mathematics interests mathematicians because of its elegance, the intrinsic aesthetics or inner beauty, which is hard for anyone to articulate.
	www.startsurfing.com /encyclopedia/m/a/t/Mathematics.html (2920 words)

	Mathematics (Site not responding. Last check: 2007-10-24)
		Mathematics is usually regarded as an important tool for science, even though the development of Mathematics is not necessarily done With science in mind (See pure mathematics and applied mathematics.).
		Nowadays Mathematics is the investigation of axiomatically defined abstract structures using mathematical notation, symbols, and logic.
		Mathematics might accordingly be seen as an extension of spoken and written natural languages, With an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships.
	mathematics.iqnaut.net (2733 words)

	[No title]
		Most contributors, however, begin with mathematical, historical and sociological considerations that also include the prospective effects of new ways of communication and publishing, which might threaten mathematical rigour. Yet a philosophical analysis of the debate and a classification of the various opinions is still lacking.
		But if mathematics is to rejuvenate itself and break new ground it will have to allow for the exploration of new ideas and techniques which, in their creative phase, are likely to be dubious as in some of the great eras of the past.
		Indeed mathematics is acquitted of one important element of physical theory, to wit, the approximation of physical facts by a mathematical model.
	philsci-archive.pitt.edu /archive/00000286/00/lakps.doc (10116 words)

	Von Neumann's "The Mathematician" Part 2 (Site not responding. Last check: 2007-10-24)
		After all, classical mathematics was producing results which were both elegant and useful, and, even though one could never again be absolutely certain of its reliability, it stood on at least as sound a foundation as, for example, the existence of the electron.
		The difference between these, on one hand, and mathematics, on the other, goes on, clearly increasing as one passes from the theoretical disciplines to the experimental ones and then from the experimental disciplines to the descriptive ones.
		As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from "reality" it is beset with very grave dangers.
	www-groups.dcs.st-and.ac.uk /history/Extras/Von_Neumann_Part_2.html (2613 words)

	3. Revolution in Logic
		Thus mathematics is seen to be in large part formalisable, and the status of its truths (as to whether they are truths of logic) is inherited from the foundation system.
		It is necessary for the development of mathematics to use axiomatic theories rather than definitions, and we find that axiomatic theories fall short of providing wholly adequate characterisations of the subject matters of mathematics.
		This showed that mathematical truth is not fully formalisable, and in consequence, either that logical truth is not formalisable or that mathematical truth goes beyond logical truth.
	www.rbjones.com /rbjpub/www/books/philrev/node4.htm (3867 words)

	Math Area (Site not responding. Last check: 2007-10-24)
		Mathematics is often defined as the study of certain subjects, such as quantity, structure, space, and change.
		The mathematics arising from this immediately has relevance for the subject which inspired it and can be applied to solve problems in that subject.
		Mathematics is inspiring to mathematicians because it has some intrinsic aesthetics or inner beauty, which is hard to explain.
	www.math-area.com (2719 words)

	Random House Trade \| The Value of Science by Henri Poincare
		Even if these consequences are challenged, it must be granted that mathematical reasoning has of itself a kind of creative virtue, and is therefore to be distinguished from the syllogism.
		Beginners are not prepared for real mathematical rigour; they would see in it nothing but empty, tedious subtleties.
		If mathematics had no other instrument, it would immediately be arrested in its development; but it has recourse anew to the same process—i.e., to reasoning by recurrence, and it can continue its forward march.
	www.randomhouse.com /randomhouse/catalog/display.pperl?isbn=9780375758485&view=excerpt (1704 words)

	Philosophy of Mathematics
		Russell's theory of types may have been the first significant advance in mathematical rigour not to have been taken into the practice of mathematics.
		Mathematics was henceforth, though in principle derivable in these formal systems, in practice developed as informally as ever.
		It is clear in the practical use of computers for proving mathematical theorems and developing mathematical systems, that the criteria by which the truth of a conjecture is judged, and the means whereby it is established, differ between mathematics (pure or applied) and most other sciences.
	www.rbjones.com /rbjpub/philos/maths/inter004.htm (681 words)

	Cramer_Harald biography (Site not responding. Last check: 2007-10-24)
		He embarked on a course of study which involved both chemistry and mathematics and at first the chemistry seemed to be at least as important to him as the mathematics.
		Cramér became interested in the rigorous mathematical formulation of probability in work of the French and Russian mathematicians such as Paul Lévy, Sergei Bernstein, and Aleksandr Khinchin in the early 1930s, but in particular the axiomatic approach of Kolmogorov.
		In this classic of statistical mathematical theory, Harald Cramér joins the two major lines of development in the field: while British and American statisticians were developing the science of statistical inference, French and Russian probabilists transformed the classical calculus of probability into a rigorous and pure mathematical theory.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Cramer_Harald.html (1091 words)

	In The Neighborhood of Mathematical Space, by Karen Shenfeld
		A mathematical work, he held, could be judged fairly on the basis of its depth and its breadth -- both of which criteria could be applied to either a discussion of a single theorem or the accumulated achievements of a lifetime.
		By the fifth century B.C., the Pythagoreans recognized that nature's design was mathematical, that mathematics -- the truths of which were discovered by means of deductive reasoning -- was therefore the key to unlocking her secrets.
		Riemann's concept of a mathematical space or manifold was born of the fundamental workings of "analytic geometry" (which represents curves by means of algebraic equations).
	at.yorku.ca /t/o/p/c/02.dir/6.htm (17907 words)

	EMail Msg <"swan.cl.ca.893:13.04.93.21.40.32"@cl.cam.ac.uk> (Site not responding. Last check: 2007-10-24)
		The influence of Bourbaki on the accepted structure of mathematics surely goes beyond a few bits of arcane terminology like "quasi-compact", and has substantially altered the emphasis placed on certain areas, e.g.
		For example, the logicists Russell and Whitehead stretched the notion of `logical' to incorporate the Axiom of Infinity; the formalist Gentzen stretched the concept of `finitary' to attain a consistency proof for arithmetic.
		Intuitionists tended to be less flexible, but they were intent not on codifying existing mathematics, but with creating a new mathematics.
	theory.stanford.edu /people/uribe/mail/qed.messages/8.html (347 words)

	Math Forum: Ask Dr. Math: A Mathematical Essay
		And thus, circa 1872, infinitesimals were purged from the accepted mathematical literature and epsilon-delta limits were used to define integrals, derivatives, convergent sequences, and all similar notions.
		In the fall of 1960 it occurred to me that the concepts and methods of contemporary Mathematical Logic are capable of providing a suitable framework for the development of the Differential and Integral Calculus by means of infinitely small and infinitely large numbers.
		So powerful is this principle that sometimes nonstandard analysis is considered a branch of mathematical logic, because it is possible to bypass practically all of the ultrafilter construction of the hyperreals and instead jump in with transfer.
	mathforum.org /dr.math/faq/analysis_hyperreals.html (9036 words)

	OUP: UK General Catalogue
		Part III is therefore about numerical linear algebra, while Part IV treats a selection of non-linear or complex problems: resolution of linear equations and systems, ordinary differential equations, single step and multi-step schemes, and an introduction to partial differential equations.
		The book has been written having in mind the advanced undergraduate students in mathematics who are interested in the spice and spirit of numerical analysis.
		It will also be useful to scientists and engineers wishing to learn what mathematics has to say about the reason why their numerical methods work - or fail.
	www.oup.com /uk/catalogue/?ci=9780198502791&view=00&promo=jan0575 (480 words)

	Top20Math.com - Online Directory for Math Education.
		There is now mathematics which can solve problems on heat and light, for example.
		In order to do so, mathematical physics has had to provide a bridge to fundamental mathematical areas.
		Mathematical innovations in the last hundred years have been major, of the same importance to the subject as all that had been developed in the years that went before.
	www.top20math.com (3152 words)

	Articles - Mathematical rigour (Site not responding. Last check: 2007-10-24)
		Look up Rigour in Wiktionary, the free dictionary.
		Rigour (American spelling: "rigor") has a number of meanings in relation to intellectual life and discourse.
		It occurs because cytokines and prostaglandins released as part of an immune response increase the set point for body temperature in the hypothalamus.
	www.totalorange.com /articles/Mathematical_rigour (648 words)

	Dynamics, Mechanics and Differential Equations - Cambridge University Press
		Gregory's Classical Mechanics is a major new textbook for undergraduate students in mathematics and physics.
		The effective use of a large number of case studies, shows how mathematics can be used to help address serious real-world problems.
		An advanced undergraduate introduction combining mathematical rigour with copious examples of important applications.
	www.cambridge.org /browse/browse_highlights.asp?subjectid=1078349 (367 words)

Try your search on: Qwika (all wikis)