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Topic: Unsolved problems in mathematics

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	Digital Library of Science
		Vedic Mathematics - 'Vedic' or 'Mathematics': A Fuzzy and Neutrosophic Analysis, by W. Vasantha Kandasamy, F. Smarandache
		Probleme Compilate şi Rezolvate de Geometrie şi Trigonometrie [Romanian]
		Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry, edited by M. Perez
	www.gallup.unm.edu /~smarandache/eBooks-otherformats.htm (743 words)

	Category:Unsolved problems in mathematics - Wikipedia, the free encyclopedia
		Unsolved problems in : Note: Use the unsolved tag: {{unsolvedFX}}, where " F " is any field in the sciences: and " X " is a concise "explanation" with or without links.
		This category is intended for all unsolved problems in mathematics, including Conjectures.
		There may or may not be conjectures for all unsolved problems.
	en.wikipedia.org /wiki/Category:Unsolved_problems_in_mathematics (128 words)

	Hilbert's problems
		Hilbert's problems are a list of 23 problems in mathematics put forth by David Hilbert in the Paris conference of the International Congress of Mathematicians in 1900.
		The problems were all unsolved at the time, and several of them turned out to be very influential for twentieth-century mathematics.
		They also list the 18th problem as "open" in their 2000 book, because the sphere-packing problem (also known as the Kepler conjecture) was unsolved, but a solution to it has now been claimed (see reference below).
	www.sciencedaily.com /encyclopedia/hilbert_s_problems (474 words)

	Unsolved problems in mathematics - Wikipedia, the free encyclopedia
		This article describes some currently unsolved problems in mathematics.
		The seven Millennium Prize Problems set by the Clay Mathematics Institute are:
		See also those problems listed as conjectures ( list of conjectures).
	en.wikipedia.org /wiki/Unsolved_problems_in_mathematics (132 words)

	Mathematical Problems by David Hilbert (Site not responding. Last check: 2007-10-17)
		The deep significance of certain problems for the advance of mathematical science in general and the important role which they play in the work of the individual investigator are not to be denied.
		This problem is solved in the main by the keen methods of H. Schwarz, C. Neumann, and Poincaré for the differential equation of the potential.
		For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments.
	aleph0.clarku.edu /~djoyce/hilbert/problems.html (12685 words)

	Learn more about Unsolved problems in physics in the online encyclopedia. (Site not responding. Last check: 2007-10-17)
		Some of these problems are theoretical, meaning that existing theories seem incapable of explaining some observed phenomenon or experimental result.
		Others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.
		The equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei.
	www.onlineencyclopedia.org /u/un/unsolved_problems_in_physics.html (573 words)

	Mathematics Links
		This is the mathematical equivalent of "six degrees of Kevin Bacon".
		Clay Mathematics Institute site is offering a $7million prize fund for the solution of the 7 most important problems in mathematics.
		Yes, there is such a thing as mathematical humour, although some of it is not in the same league as Woody Allen.
	www.simonsingh.net /Mathematics_Links.html (662 words)

	Felix On-line (Site not responding. Last check: 2007-10-17)
		Much of the mathematical research in the 20th century has been influenced by this list of unsolved problems, as both successful and unsuccessful attempts at solutions have yielded a number of important discoveries on the way.
		The list of problems itself has been carefully selected to include not only the most difficult ones, but also the ones whose solutions would have a relevance to areas of mathe-matics and the other sciences beyond the one in which the problem was originally for-mulated, hopefully leading to further serendipitous discoveries en route.
		Generally speaking, problems that are in P are easy to solve, while problems in NP are difficult to solve, but significantly, given an answer to an NP problem, it is easy to verify whether it is indeed a solution.
	www.felixonline.co.uk /2002-04/article.php?aid=1988 (1464 words)

	All About what I wanted to know more!: List of unsolved mathematical problems
		Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'.
		Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships.
		Clay Mathematics Institute The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Cambridge, Massachusetts, and dedicated to increasing and disseminating mathematical knowledge.
	rajpalrao.blogspot.com /2004/09/list-of-unsolved-mathematical-problems.html (802 words)

	Clay Public Lecture: Are the unsolved problems in mathematics — Barry Mazur
		The Riemann Hypothesis, is one of the Clay Mathematics Institute's $1 million Millennium Prize Problems.
		The aim of this lecture series is to increase the awareness and understanding of mathematics — in the public at large as well as in the business, scientific and university communities.
		How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.
	www.claymath.org /public_lectures/mazur.php (266 words)

	Amazon.com: Books: The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time (Site not responding. Last check: 2007-10-17)
		The author is aware of the difficulty in describing the content of the problems to readers without substantial mathematical preparation, and he does a good job in general.
		One can of course think of many other problems that fit the stature of the millennium problems, such as the invariant subspace conjecture, or developing a complete mathematical model of the cell, but these seven will no doubt spark the curiosity of a few young persons as they further their studies in mathematics.
		The mathematics needed for a precise statement of the conjecture is fairly daunting, but his informal description conveys the heart of it vividly and accurately.
	www.amazon.com /exec/obidos/tg/detail/-/0465017290?v=glance (2561 words)

	Difficult solutions yield monetary rewards - The Triangle - Sci-Tech (Site not responding. Last check: 2007-10-17)
		In the year 2000, the Clay Institute of Mathematics issued seven unsolved problems that are very important for the development of mathematics in the future.
		The problem formulated by Cook and Levin is the P (easy to find) vs. NP (easy to check) in 1971 and is yet unsolved, and the million dollar prize is waiting for those who can solve it.
		The problem is to describe these equations with a rigorous mathematical theory, because all of the current knowledge is based only on experiments.
	www.thetriangle.org /news/2005/05/27/SciTech/Difficult.Solutions.Yield.Monetary.Rewards-954396.shtml (1389 words)

	Millennium Prize Problems
		During the Millennium Meeting held on May 24, 2000 at the Collège de France, Timothy Gowers presented a lecture entitled The Importance of Mathematics, aimed for the general public, while John Tate and Michael Atiyah spoke on the problems.
		The rules for the award of the prize have the endorsement of the CMI Scientific Advisory Board and the approval of the Directors.
		Formulated in his 1859 paper, the Riemann hypothesis in effect says that the primes are distributed as regularly as possible given their seemingly random occurrence on the number line.
	www.claymath.org /millennium (350 words)

	Slav
		A Russian mathematician is reporting that he has proved the Poincaré Conjecture, one of the most famous unsolved problems in mathematics.
		The mathematician, Dr. Grigori Perelman of the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, is describing his work in a series of papers, not yet completed.
		In the 1950's, however, a Russian mathematician proved that the problem was impossible to resolve in four dimensions and that even for three dimensions, the question looked hopelessly complex.
	www.network54.com /Forum/thread?forumid=221692&messageid=1051186900&lp=1058783490 (1756 words)

	The New York Review of Books: 'A MATTER OF TEMPERAMENT'
		It so happens that I was a student of Mathematical logic in Göttingen (Hilbert's University) in 1931–33, just after the publication of the famous 1931 paper by Gödel. Hence I venture to reply.
		He held that the problems of mathematics can all ultimately be solved: this he formulated in a famous speech in the words "Wir müssen wissen; wir werden wissen." (We must know, we will know).
		He believes that the reduction of mathematical concepts to their abstract logical components is the main road of progress in understanding.
	www.nybooks.com /articles/1780 (1020 words)

	Unsolved Problems in Number Theory
		Number theory requires very little advanced mathematical knowledge or training, all that is required is a strong knowledge of algebra, and an understanding of numbers.
		I hope this collection of problems will encourage and excite you about the potentials of mathematics, or if you are already interested than I hope you find new and interesting problems to explore.
		All that I ask is that if you complete my work on a problem, and a paper results from this work, that I be informed and included as a joint author if I had already made a significant contribution to the problem.
	www.geocities.com /mo43speep (212 words)

	Open Problems for Undergraduates (Site not responding. Last check: 2007-10-17)
		This is a collection of open problems in Discrete Mathematics which are currently being researched by members of the DIMACS community.
		These problems are easily stated, require little mathematical background, and may readily be understood and worked on by anyone who is eager to think about interesting and unsolved mathematical problems.
		Although these problems are intended for undergraduates, it is expected that high school students, teachers, graduate students and professional mathematicians will be drawn to this collection.
	dimacs.rutgers.edu /~hochberg/undopen (138 words)

	Ideas, Concepts, and Definitions (Site not responding. Last check: 2007-10-17)
		In a community of mathematicians, an open problem is a question that no one has found the answer to.
		Anyone who does mathematics for very long soon discovers that open problems are abundant, and even more of them are generated as mathematicians think about something and ask themselves questions in an effort to understand it.
		Sometimes an open problem becomes famous because, as it is shared with larger and larger communities of mathematicians, more and more people get curious and work on it, but still the solution is elusive.
	www.c3.lanl.gov /mega-math/gloss/math/openpr.html (266 words)

	Mathematical Problems of David Hilbert (Site not responding. Last check: 2007-10-17)
		In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century.
		In 1974 a symposium was held at Northern Illinois University on the Mathematical developments arising from Hilbert problems.
		The two-volume proceedings of the symposium was edited by Felix Browder and published by the American mathematical Society in 1976.
	babbage.clarku.edu /~djoyce/hilbert (363 words)

	International Mathematics Olympiad
		The Bay Area Mathematical Olympiad (BAMO) is a contest for high school students sponsored jointly by the Mathematical Sciences Research Institute (MSRI), the American Institute of Mathematics (AIM), the University of California at Berkeley (UCB), and the University of San Francisco (USF).
		The Colorado Mathematical Olympiad (CMO) is the largest essay-type mathematical competition in the United States, with 600 to 1,000 participants competing annually for fine prizes.
		The Olimpíada Matemática Argentina (OMA) is the Argentinian Mathematics Olympiad.
	olympiads.win.tue.nl /imo (2183 words)

	Unsolved Problems on Mathematics for the 21st Century (Edited by: J.M. Abe and S. Tanaka) (Site not responding. Last check: 2007-10-17)
		Unsolved Problems on Mathematics for the 21st Century (Edited by: J.M. Abe and S. Tanaka)
		Unsolved Problems on Mathematics for the 21st Century
		“Unsolved Problems on Mathematics for the 21st Century - A Tribute to Kiyoski Iséki’s 80th Birthday” is a book dedicated to Dr. Kiyoshi Iséki for his contribution in the scientific, academic and public community.
	www.iospress.nl /html/9051994907.php (134 words)

	Amazon.ca: Books: Unsolved Problems in Number Theory (Site not responding. Last check: 2007-10-17)
		Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of disciplines where mathematics is applied.
		This book provides a steady supply of easily understood, if not easily solved, problems which can be considered in varying depths by mathematicians at all levels of mathematical maturity.
		For this new edition, the author has included new problems on symmetric and asymmetric primes, sums of higher powers, Diophantine m-tuples, and Conway's RATS and palindromes.
	www.amazon.ca /exec/obidos/ASIN/0387208607 (243 words)

	BBC NEWS \| Science/Nature \| Book explains maths mysteries
		An original set of 23 mathematical problems was outlined by Prussian mathematician David Hilbert in 1900.
		Although the problems primarily mean little to non-mathematicians, they do have important practical use.
		"There are weird analogies between this very pure-sounding mathematical problem and some very deep and beautiful problems in physics," said Professor Sir Michael Berry, of Bristol University, UK, and a physicist who has worked on the Riemann hypothesis for 20 years.
	news.bbc.co.uk /1/hi/sci/tech/3430309.stm (681 words)

	Motivational Problems in Mathematics (Site not responding. Last check: 2007-10-17)
		A first-year attempting these problems should be led naturally to develop intuition through examples, to test conjectures, and to find reasoning/proofs more powerful than is required for these questions.
		These problems were selected because they are interesting, they can be stated with few prerequisites, and they have been solved.
		About a quarter of these problems were taken from the Conjecture and Proof course in the Budapest Semesters in Mathematics program.
	www.math.columbia.edu /~zare/motmath8.html (252 words)

	Unsolved Problems in Geometry (Problem Books in Mathematics / Unsolved Problems in Intuitive Mathematics) - Hotel ... (Site not responding. Last check: 2007-10-17)
		After the counting numbers, geometry is the oldest branch of mathematics and no doubt the first one that required abstract thinking.
		The range of problems that fall under the geometric umbrella is extremely wide and some even have practical uses.
		This book is a testament to the wide range of problems that are geometric in nature.
	www.hotelresource.com /bookstore/asinsearch_0387975063.html (172 words)

	Unsolved problems in mathematics - Wikipedia
		WÃ¤hle â Unsolved problems in mathematics suchen â um nach Unsolved problems in mathematics zu suchen.
		Falls Du diese Seite soeben erstellt hast, kann es sein, dass die Aktualisierung der Datenbank verzÃ¶gert wurde.
		Ein WÃ¶rterbucheintrag zu Unsolved problems in mathematics hat seinen Platz im Wiktionary ( Wiktionary).
	de.wikipedia.org /wiki/Unsolved_problems_in_mathematics (145 words)

	Tutor4Math.com > Resources (Site not responding. Last check: 2007-10-17)
		Mathematical Problems - In various subjects, compiled by Torsten Sillke.
		Unsolved Mathematics Problems - Compiled by Steven Finch.
		Unsolved Problem of the Week Archive - A list of unsolved problems published by MathPro Press during 1995.
	tutor4math.com /odp.php?browse=/Science/Math/Research/Open_Problems (167 words)

	UNSOLVED PROBLEMS AND REWARDS
		The problem has been solved in the affirmative: the binary word R does indeed contain every binary word infinitely many times.
		The problem is to prove or disprove that every positive integer will eventually be written during the counting procedure.
		The problem is to prove or disprove that proposition.
	faculty.evansville.edu /ck6/integer/unsolved.html (1070 words)

	Unsolved Problems
		Some of these problems have been solved (and thus the title is slightly incorrect) and I won't claim to be familiar with all current results.
		Julio Subocz notes that this is also called Berge's conjecure or the Berge-Sauer conjecture and, in a conference in Lisboa (November 1995), Y. Hamidoune cited a proof (approximately 65 pages) by Taskinov of the conjecture.
		In 1975, P. Erdos proposed the problem of determining the maximum number $f(n)$ of edges in a simple graph of $n$ vertices in which any two cycles are of different lengths.
	www.math.fau.edu /locke/unsolved.htm (3001 words)

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