1. Unsolved Problems unsolved problems. You can contact Stephen C. Locke at LockeS@fau.edu. Several people have asked me about unsolved problems. I http://www.math.fau.edu/locke/unsolved.htm

Unsolved Problems You can contact Stephen C. Locke at LockeS@fau.edu Several people have asked me about unsolved problems. I will take the easy way out: see the list of 50 problems in Bondy and Murty . You can now see the list as it originally appeard in the the text, Graph Theory with Applications . (May, 2004: The authors are writing the next edition of the book.) 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. If you find that one of them has been solved (or even that some reasonable progress has been made), please e-mail me . Also, I'm not giving you all of the references in Bondy and Murty . You should get yourself a copy of that book (or look at the online version). Problems 26-56 Problems 57-61 Problems number above 50 on my list are from sources other than the Bondy and Murtry text. The reconstruction conjecture . (S.M. Ulam, 1960) 2. A graph G is embeddable in a graph H if G is isomorphic to a subgraph of H . Characterise the graphs embeddable in the k -cube. (V.V. Firsov, 1965)

2. Mathsoft: Mathsoft Unsolved Problems s of some unsolved problems and numerous links to other collections.......Compiled by Steven Finch. http://www.mathsoft.com/mathresources/problems/

search site map about us  + news  + ... Statistics Resources Unsolved Problems Mathsoft Constants Engineering Standards Engineering Links Math Resources Welcome! This evolving collection of unsolved mathematics problems is not systematic or complete; it is only an eclectic gathering of questions and partial answers which have come to my attention over the years. Unsolved Problems on Other Sites On a Generalized Fermat-Wiles Equation Zero Divisor Structure in Real Algebras Sleeping Habits of Armadillos ... contact us

3. Unsolved Problems In Function Theory Notes by Alexandre Eremenko. http://www.math.purdue.edu/~eremenko/uns.html

My favorite unsolved problems GEOMETRIC FUNCTION THEORY AND POTENTIAL THEORY: ps pdf Some constants studied by Littlewood (Updated Oct 2002). ps pdf Exceptional set in Gross' Theorem. ps pdf "Hawaii Conjecture" (attributed to Gauss). ps pdf Does every universe contain a place where you can stay at rest? (Lee Rubel) ps pdf Erdos' problem on the length of lemniscates (at least $200 prize). DIFFERENTIAL EQUATIONS AND ITERATION IN THE COMPLEX DOMAIN: ps pdf Wandering domains of entire functions. TRANSCENDENTAL HOLOMORPHIC CURVES: ps pdf Modified Cartan's Conjecture. ps pdf Holomorphic curves with few inflection points. RATIONAL FUNCTIONS AND RATIONAL CURVES: ps pdf Rational curves with real inflection points (B. and M. Shapiro, for more info, see F. Sottile's page Other interesting items in this site: Progress report on some problems from Hayman's Collection When function theory became an obsolete subject? (Excerpt from a letter of Mittag-Leffler to Kowalevski.) What is mathematics? Some expert's opinions. jokes related to complex analysis some problems, whose solutions I do know (level: undergraduate+) stories about ODE, calculus and history

4. Unsolved Problems Mathematical research often concerns questions which are so abstract and technically complicated that only a small number of experts in that particular field can fully understand the problems and their significance. a handful of problems which to my knowledge and to this date are still unsolved although they can http://abel.math.umu.se/~frankw/unsolved.html

Mathematical research often concerns questions which are so abstract and technically complicated that only a small number of experts in that particular field can fully understand the problems and their significance. Therefore one is easily led to the conclusion that every problem is difficult to understand. This is not so. On this page I have gathered a handful of problems which to my knowledge and to this date are still unsolved although they can be understood by any one who has a working knowledge of, say, the high-school mathematics curriculum. Can every even integer number greater be written as the sum of two prime numbers? We have for example that: and so on, but is it true for every even number? Nobody knows, but most mathematicians seem to think that it is true. (The conjecture is known to be true for all even integers less than 20 000 000 000 or so. It is also known that every "sufficiently large" even integer can be written as the sum of a prime number and an integer with at most two prime factors.) Two consecutive odd numbers which are both prime are called twin primes, e.g. 5 and 7, or 41 and 43, or 1,000,000,000,061 and 1,000,000,000,063. But is there an infinite number of twin primes?

5. Unsolved Problems In OR unsolved problems in OR. This page contains a list of open problems that I find intriguing. They are not as difficult or as significant http://www.statslab.cam.ac.uk/~rrw1/research/unsolved.html

Unsolved Problems in OR This page contains a list of open problems that I find intriguing. They are not as difficult or as significant as the question of whether P does or not equal NP. But these are problems that are easy to state and understand, but whose solution has defied the efforts of good researchers over a number of years. Most of these problems are in the realm of stochastic optimization. I would love to see a solution to any of these problems. This page is under construction. I plan to write something about the following problems, and others, in due course. The bomber problem See description The rendezvous problem See description Search for a moving target See abstract Non-preemptive release of stochastic jobs to uniform machines See abstract The unimportance of inserted idle time in non-preemptive stochastic scheduling to minimize flow time on parallel machines home page

6. Mathsoft: Mathsoft Unsolved Problems: Unsolved Problems On Other Sites unsolved problems on Other Sites. Jeff Martin); Richard Weber s unsolved problems in Operations Research (University of Cambridge); http://www.mathsoft.com/mathresources/problems/article/0,,1999,00.html

search site map about us  + news  + ... Unsolved Problems Unsolved Problems Links On a Generalized Fermat-Wiles Equation Zero Divisor Structure in Real Algebras Sleeping Habits of Armadillos Mathsoft Constants ... Math Resources Unsolved Problems on Other Sites Jeff Lagarias' 3x+1 problem and related problems The Generalized 3x+1 Mapping (University of Queensland) and 1999 Conference on the Collatz Problem Proceedings Alex Lopez-Ortiz's sci.math FAQ on Famous Problems in Mathematics (University of New Brunswick) Chris Caldwell's Riemann Hypothesis (University of Tennessee at Martin); also Daniel Bump's Riemann Hypothesis (Stanford University) and Barry Cipra's A Prime Case of Chaos MathPro Press Unsolved Math Problem of the Week column and General References Twin Primes Conjecture and Goldbach's Conjecture, discussed in Prime Numbers: Some Unsolved Problems , part of MacTutor History of Mathematics (University of St Andrews); also Chris Caldwell's Prime Conjectures and Open Questions (University of Tennessee at Martin) Jan Otto Munch Pedersen's Known Amicable Pairs (Vejle Business College, Denmark) and Chris Caldwell's

7. Unsolved Problems And Conjectures Regarding equal sums of like powers, compiled by Chen Shuwen. http://member.netease.com/~chin/eslp/unsolve.htm

Equal Sums of Like Powers Unsolved Problems and Conjectures The Prouhet-Tarry-Escott Problem a k + a k + ... + a n k = b k + b k + ... + b n k k n Is it solvable in integers for any n Ideal solutions are known for n = 1, 2, 3, 4, 5, 6, 7, 8 ,9, 11 and no other integers so far. How to find new solutions for n = 10 and How to find the general solution for n The general solution is known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) only. The complete symmetric solution have been found for ( k = 1, 2, 3, 4 ) How to find a new solution of the type ( k =1, 2, 3, 4, 5, 6, 7, 8 ) How to find non-symmetric ideal solutions of ( k =1, 2, 3, 4, 5, 6, 7, 8 ) and ( k =1, 2, 3, 4, 5, 6, 7, 8, 9 ) How to find a solution chain of the type ( k = 1, 2, 3, 4 ) a a a a a b b b b b c c c c c ( k = 1, 2, 3, 4 ) Solution chains are known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) and ( k = 1, 2, 3, 4, 5 ) so far. Some other open problems are present on Questions by Lander-Parkin-Selfrige (1967) a k + a k + ... + a m k = b k + b k + ... + b n k Is ( k m n ) always solvable when m n k Is it true that ( k m n ) is never solvable when m n k For which k m n such that m n k is ( k m n ) solvable ?

8. Some Unsolved Problems To my knowledge they are all unsolved. Of course, this is not a complete list of all unsolved problems in mathematics. For instance http://www.math.unibas.ch/~winkel/problem.html

Some Mathematical Problems This is a collection of some mathematical questions, which I encountered somehow, mostly in the context of my own research. To my knowledge they are all unsolved. Of course, this is not a complete list of all unsolved problems in mathematics. For instance, I omitted those problems which everybody knows anyway (like the Jacobi conjecture). Furthermore the choice is made following my personal taste and prejudices. I certainly do not want to claim that these are the most important problems in today mathematics. Nevertheless, I am very curious about the problems listed below. If anybody is able to solve one or more or knows some results in these directions, please tell me. Does there exists a compact Riemann surface M of genus at least two which can be embedded into a quotient of SL C by a discrete cocompact subgroup? (This is a question raised by A.T.Huckleberry.) Remark: This question is discussed in my Book on parallelizable manifolds and some partial results are derived. In particular, such a curve can never arise as a zero-section of a rank two vector bundle. Let S be a complex semisimple Lie group

9. UNSOLVED PROBLEMS AND REWARDS unsolved problems and Rewards. Richard K. Guy, unsolved problems in Number Theory, second edition, SpringerVerlag, 1994. The problem originates in. http://faculty.evansville.edu/ck6/integer/unsolved.html

Unsolved Problems and Rewards Stated below are a few challenging problems. If you are first to publish a solution, let me know, and collect your reward! 1. The Kolakoski sequence: This sequence is is identical to its own runlength sequence. Reward: $200.00 for publishing a solution of any one of the five problems stated in Integer Sequences and Arrays. The sequence originates in William Kolakoski , "Self generating runs, Problem 5304," American Mathematical Monthly 72 (1965) 674. For a proof that the Kolakoski sequence is not periodic, see the same Monthly See also Kolakoski Sequence (Eric Weisstein's The World of Mathematics 2. A Shuffle. Is every positive integer a term of this sequence: Reward: $300.00. To see how to generate the sequence, visit Kimberling Sequence (Eric Weisstein's The World of Mathematics For a discussion and variant of the problem, see Richard K. Guy Unsolved Problems in Number Theory, second edition , Springer-Verlag, 1994. The problem originates in C. Kimberling, Problem 1615

10. Alexandre Eremenko Home Page Papers and Recent preprints (available in ps and pdf format) Some unsolved problems Some solved problems Stories and problems about ODE, calculus and history http://www.math.purdue.edu/~eremenko/

Alexandre Eremenko picture Mathematics Department, Purdue University 150 N. University Street West Lafayette, IN 47907-2067 OFFICE: Math 612 PHONE: (765)494-1975, FAX: (765)494-0548 EMAIL: eremenko@math.purdue.edu vita Papers and Recent preprints (available in ps and pdf format) Some unsolved problems Some solved problems Stories and problems about ODE, calculus and history of science. CO-AUTHORS: A. Atzmon, A. Baernstein II, I. N. Baker, W. Bergweiler (3), V. Boichuk, M. Bonk J. Clunie, N. Eremenko, A. Fryntov, B. Fuglede, A. Gabrielov (5), Yu. Gaida, A. A. Goldberg (6), D. Hamilton, W. Hayman (4), J. Langley (2), L. Lempert, G. Levin (3), J. Lewis , T. Lyons, M. Lyubich S. Merenkov D. Novikov (2), I. Ostrovskii (3), M. Ostrovskii, M. Petrika, J. Rossi (2), L. Rubel (2), D. Shea, M. Sodin (16), A. Solynin. (My Erdos number: is 2). OTHER SITES Math. Journal Price Survey MAG journal (Kharkov) Joseph Fourier Portraits of Gauss Misha Gromov John Milnor ... Minimal surface Museum of Matthias Weber XXX archive (Los Alamos) Jahrbuch uber die Fortschritte der Mathematik Conference pictures

11. Unsolved Problem Of The Week Archive A list of unsolved problems published by MathPro Press during 1995. http://cage.rug.ac.be/~hvernaev/problems/archive.html

Unsolved Problem of the Week Archive Welcome to the archive for the Unsolved Math Problem of the Week Each week, for your edification, we publish a well-known unsolved mathematics problem. These postings are intended to inform you of some of the difficult, yet interesting, problems that mathematicians are investigating. We give a reference so that you can get more information about the topic. These problems can be understood by the average person. Nevertheless, we do not suggest that you tackle these problems, since mathematicians have been unsuccessfully working on these problems for many years. Should you wish to discuss aspects of these problems with others, one of the newsgroups, such as sci.math , might be the appropriate forum. 3-Sep-1995 Problem 36 : Primes of the form n^n+1 27-Aug-1995 Problem 35 : Must one of n points lie on n/3 lines? 20-Aug-1995 Problem 34 : Squares with Two Different Decimal Digits 13-Aug-1995 Problem 33 : Unit Triangles in a Given Area 6-Aug-1995 Problem 32 : Can the Cube of a Sum Equal their Product 30-Jul-1995 Problem 31 : Different Number of Distances 23-Jul-1995 Problem 30 : Sum of Four Cubes 16-Jul-1995 Problem 29 : Fitting One Triangle Inside Another 9-Jul-1995 Problem 28 : Expressing 3 as the Sum of Three Cubes 2-Jul-1995 Problem 27 : Factorial that are one less than a Square 25-Jun-1995 Problem 26 : Inscribing a Square in a Curve 18-Jun-1995 Problem 25 : The Collatz Conjecture 11-Jun-1995 Problem 24 : Primes Between Consecutive Squares 4-Jun-1995 Problem 23 : Thirteen Points on a Sphere 28-May-1995

12. Overview Of "Mathematician's Secret Room" unsolved problems in Number Theory. English and Japanese text by Hisanori Mishima. http://www.asahi-net.or.jp/~KC2H-MSM/mathland/overview.htm

Overview of "Mathematician's Secret Room" Challenges to the Unsolved Problems in Number Theory (May 17, 2004) (Chapter 2, 4, 9, 10, Appendix 1, 4 are translated in English. Other chapters are still written only in Japanese, sorry.) Chapter 4 : A solution of case n=52 for n=x +y +z was added. Chapter 2 : Search range for patterns not including zero were extended up to 10 . (May 17, 2004) (For patterns including zero, up to 10 were serached.) (June 04, 2001) : In Chapter 7, new results by Tomas Oliveira and Silva. Their web site is here ( 3x+1 conjecture verification results Chapter 0 : Opening Why I had an interest in Number Theory. Chapter 1 : 4/n = 1/a + 1/b + 1/c whether do there exist the natural number solutions of above equation, or not. I found the construction method of the parameterize solution from arbitrary solutions. That is, Theorem : Let A, B, C in N be a solution of following Diophantine equation, m/P=1/A+1/B+1/C, B=kP (m=4, 5, 6, 7, P=prime, k in N (i.e. 2 of A, B, C can be divisable by P) Define a, b, c, d, e, f, c', d' as

13. Unsolved Problems From MathWorld unsolved problems from MathWorld There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/UnsolvedProblems.h

14. Unsolved Problems -- From MathWorld unsolved problems. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture. http://mathworld.wolfram.com/UnsolvedProblems.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Mathematical Problems Unsolved Problems Unsolved Problems There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture 2. The Riemann hypothesis 3. The 4. The conjecture that there exists a Hadamard matrix for every positive multiple of 4. 5. The twin prime conjecture (i.e., the conjecture that there are an infinite number of twin primes 6. Determination of whether NP-problems are actually P-problems 7. The Collatz problem 8. Proof that the 196-algorithm does not terminate when applied to the number 196. 9. Proof that 10 is a solitary number 10. Finding a formula for the probability that two elements chosen at random generate the symmetric group 11. Solving the

15. Open Problems List A collection of papers outlining unsolved problems in the field of dynamical systems. http://www.math.sunysb.edu/dynamics/open.html

Open Problems in Dynamical Systems Open problems in holomorphic dynamics Two lists of problems are currently available on-line: Conformal Dynamics Problem List Ed. by B. Bielefeld, IMS at Stony Brook Preprint 1990/1 and more recent Problems in Holomorphic Dynamics Ed. by B. Bielefeld and M. Lyubich, IMS at Stony Brook Preprint 92/7 In addition some open questions may be found in these surveys Open problems in dynamics in several complex variables is a part of Several complex variables problems list available from Several complex variables preprint server in Indiana. Please send your problems to Gregery Buzzard at gbuzzard@iu-math.math.indiana.edu Problems in Low-Dimensional Topology a 380 pages PostScript file edited by Rob Kirby contain some problems on Topological Dynamics. Topology of hyperbolic attractors. A problem submitted by Christian Bonatti. A collection maintained by Sergiy Kolyada and Michal Misiurewicz Is entropy effectively computable? A problem by John Milnor We are soliciting open problems in various areas of Dynamical Systems for posting on this page. You can post a problem by filling out this form or by sending an e-mail to webmaster@math.sunysb.edu

16. [gr-qc/0107090] Current Trends In Mathematical Cosmology A review of current unsolved problems in mathematical cosmology http://arxiv.org/abs/gr-qc/0107090

General Relativity and Quantum Cosmology, abstract gr-qc/0107090 From: Spiros Cotsakis [ view email ] Date ( ): Fri, 27 Jul 2001 17:32:02 GMT (13kb) Date (revised v2): Sat, 28 Jul 2001 14:53:55 GMT (13kb) Current Trends in Mathematical Cosmology Authors: Spiros Cotsakis Comments: 16 pages, LaTeX. To appear in the Proceedings of the 2nd Hellenic Cosmology Workshop, (Kluwer, 2001) We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current, seemingly unrelated trends of this subject. We discuss problems associated with the definition and asymptotic structure of the notion of cosmological solution and also problems related to the qualification of approximations and to the ranges of validity of given cosmologies. Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted);

17. Unsolved Problems Math Problems, Games, and Puzzles Problems. Real World Mathematics. Puzzles and Math Miscellany. unsolved problems. unsolved problems. unsolved problems in Operations Research. Unsolved http://www.spartanburg2.k12.sc.us/links/problems.htm

Math Problems, Games, and Puzzles Algorithmic Information Theory Brain Teasers Fermi Questions Library Ideas, Concepts, and Definitions ... What Good is Math?

18. Konrad Lorenz Institute For Comparative Ethology An Institute of the Austrian Academy of Sciences that investigates the major unsolved problems in behavioral and evolutionary ecology. http://www.oeaw.ac.at/klivv

About us: Main Info Reasearch: Research Program The Institute Publications Project Surumoni ... Seminar Contact: People News: Waldlehrpfad (Main info) New Projects Map ... Links For questions and contributions regarding this website please mail to: webmaster@klivv.oeaw.ac.at

19. Hilbert's Problems From MathWorld Hilbert's Problems from MathWorld A set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total, ten were presented at the Second International Congress in Paris http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/HilbertsProblems.h

20. Combinatorial Game Theory Includes Gamesman Toolkit, which implements the mathematics of twoplayer games in Winning Ways; and Richard K. Guy's paper unsolved problems in Combinatorial Games. http://www.gac.edu/~wolfe/papers-games/

Combinatorial game theory I'm beginning to write some gameboard LaTeX macros, but they are in a state of flux. In particular, I hope to design less angular drawings of some of the games and to include more general ways of marking stones and squares. Feel free to download them, and let me know what suggestions you have. In particular, what input format would you want for adding markings? The sty file, gameboard.sty requires pstricks.sty and epic.sty . The file gameboard.tex has examples. I'm happy to report that Aaron Siegel at Berkeley has written a new Combinatorial Game Suite which is a dramatic improvement over my toolkit. In particular, The Suite is designed to be more flexible and extensible. For instance, you can implement the rules to a new game by writing a plug-in without making any changes to source code. The Suite is written in Java making it portable. (It's been tested on Windows 2000/XP, Linux and Solaris.) Aaron has provided additional functionality that were not part of my toolkit distribution, such as support for loopy games and thermographs. The Suite's has an easy to use graphical user interface.

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