1. Unsolved Problems -- From MathWorld Klee, V. Some Unsolved Problems in Plane Geometry. Math. Mag. Ogilvy, CSTomorrow s math unsolved problems for the Amateur, 2nd ed. http://mathworld.wolfram.com/UnsolvedProblems.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team 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

2. Some Unsolved Problems they are all unsolved. Of course, this is not a complete list of all unsolved problems in mathematics. For instance, I omitted those problems http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Unsolved Problem Of The Week Archive Welcome to the archive for the Unsolved Math Problem of the Week. you of some of the difficult, yet interesting, problems that mathematicians http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. Unsolved Problems Unsolved Problems. You can contact Stephen C. Locke at LockeS@fau.edu. Email LockeS@fau.edu URL http//www.math.fau.edu/locke/unsolved.. .. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Article About 3 Unsolved Math Problems Article about 3 unsolved math problems 2 is about graph theory http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. Sci.math FAQ Unsolved Problems sci.math FAQ Unsolved Problems. There are reader questions on this topic! Help others by sharing your knowledge http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Unsolved Problems In Function Theory My favorite unsolved problems Prize policies when applicable, a prize for the problem will be payed with a check in US dollars to the first http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Mathproblems.info Challenging word problems, spanning basic math to differential equations. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Mathsoft Mathsoft Unsolved Problems Unsolved Problems. Mathsoft Constants. Engineering Standards. Engineering Links. Math Resources. Welcome! This evolving collection of unsolved http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Open Problems For Undergraduates background, and may readily be understood and worked on by anyone who is eager to think about interesting and unsolved mathematical problems. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Unsolved Problems TomorrowÕs math unsolved problems for the amateur, 2nd edition Charles StanleyOgilvy Oxford University Press, New York 1972 Hardcover. 198 pages. http://www.mathpropress.com/mathBooks/UnsolvedProblems.html

Unsolved Problems Algebraic GeometryOpen Problems C. Ciliberto Springer-Verlag , Berlin: 1983 Paperback. 411 pages. ISBN 0-387-12320-2 LCCN 83-012390 Continua: With the Houston Problem Book Volume 170 of the series Lecture Notes in Pure and Applied Mathematics Howard Cook, W. T. Ingram, and K. T. Kuperberg Marcel Dekker, City of publication unknown: 1995 Paperback. 402 pages. ISBN 0-8247-9650-0 Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry Florentin Smarandache Xiquan Publishing House, City of publication unknown: 2000 Paperback. 84 pages. ISBN 1-879585-74-X Erdos on Graphs: His legacy of unsolved problems Fan R. K. Chung and Ronald L. Graham A K Peters, Wellesley, MA: 1998 Hardcover. 142 pages. ISBN 1-56881-079-2 LCCN 97-046327 Mathématiques de demain, problèmes non résolus Charles Stanley Ogilvy Dunod, Paris: 1966 Unknown binding. 152 pages. French. LCCN 72-381436 Old and New Unsolved Problems in Plane Geometry and Number Theory Volume 11 of the series Dolciani mathematical expositions Victor Klee and Stan Wagon Mathematical Association of America , Washington, DC: 1991 Hardcover. 333 pages. ISBN 0-88385-315-9 LCCN 91-061591

12. Unsolved Problems: References Ogilvy 1972 C. Stanley Ogilvy, Tomorrow s math unsolved problems for theAmateur. 2nd edition. Oxford University Press. New York 1972. http://cage.rug.ac.be/~hvernaev/problems/references.html

Unsolved Problems General References The following books contain unsolved problems or are referenced by the unsolved problem of the week Especially rich are [Croft 1991] [Guy 1994] and [Klee 1991] [Beiler 1966] Albert H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertain. 2nd edition. Dover. New York: 1966. [Bondy 1976] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications. North Holland. New York: 1976. [Boroczky 1987] Intuitive Geometry. North-Holland Publishing Company. New York: 1987. [Croft 1991] Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy, Unsolved Problems in Geometry. Springer-Verlag. New York: 1991. [Dudeney 1970] H. E. Dudeney, Amusements in Mathematics. Dover. New York: 1970. [Dunham 1990] William Dunham, Journey Through Genius: The Great Theorems of Mathematics. John Wiley and Sons. New York: 1990. [Erdos 1980] Old and New Problems and Results in Combinatorial Number Theory. [Gardner 1978] Martin Gardner, Mathematical Magic Show. Vintage Books. New York: 1978. [Gardner 1983] Martin Gardner

13. Favorite Unsolved Problems Alexandre Eremenko (Purdue University). Mainly in analysis. http://www.math.purdue.edu/~eremenko/

Alexandre Eremenko picture Mathematics Department, Purdue University 150 N. University Street West Lafayette, IN 47907-2067 OFFICE: Math 450 PHONE: (765)494-1975, FAX: (765)494-0548 EMAIL: eremenko@math.purdue.edu Math 511 Linear Algebra, Fall 2005 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 (4), V. Boichuk, M. Bonk J. Clunie, N. Eremenko, A. Fryntov, B. Fuglede, A. Gabrielov (6), Yu. Gaida, A. A. Goldberg D. Hamilton, W. Hayman J. Langley L. Lempert, G. Levin (3), J. Lewis , T. Lyons, M. Lyubich S. Merenkov D. Novikov I.V. Ostrovskii (3), M.I. Ostrovskii, M. Petrika, J. Rossi (2), L. Rubel M. Shapiro, D. Shea, M. Sodin (16), A. Solynin, A. Vainshtein. (My Erdos number: is 2). OTHER SITES: Math Journals Price Crisis , Math Journals Price Survey . Free old and new journals on line: Acta math. Ann.Acad.Sci.Fenn Mathdoc (EMANI), Numdam Project Euclid MAG journal (Kharkov)

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

My favorite unsolved problems Prize policies: when applicable, a prize for the problem will be payed with a check in US dollars to the first person who sends me a complete solution which I will verify and recognize as correct. 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) $200 ps pdf Erdos' problem on the length of lemniscates (at least $200). DIFFERENTIAL EQUATIONS AND ITERATION IN THE COMPLEX DOMAIN: ps pdf Meromorphic functions satisfying certain differential equations (E. Hille) ps pdf Wandering domains of entire functions. TRANSCENDENTAL HOLOMORPHIC CURVES: ps pdf Modified Cartan's Conjecture. $300 ps pdf Holomorphic curves with few inflection points. $500 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

15. Some Unsolved Problems Mainly in analysis. By J¶rg Winkelmann. http://www.math.unibas.ch/~winkel/problem.html

16. Hilbert's Problems -- From MathWorld Hilbert s problems are a set of (originally) unsolved problems in mathematicsproposed Concerning the Hilbert 16th Problem. Providence, RI Amer. math. http://mathworld.wolfram.com/HilbertsProblems.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Mathematical Problems Problem Collections ... Unsolved Problems Hilbert's Problems Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert . Of the 23 total appearing in the printed address, ten were actually presented at the Second International Congress in Paris on August 8, 1900. In particular, the problems presented by Hilbert were 1, 2, 6, 7, 8, 13, 16, 19, 21, and 22 (Derbyshire 2004, p. 377). Furthermore, the final list of 23 problems omitted one additional problem on proof theory (Thiele 2001). Hilbert's problems were designed to serve as examples for the kinds of problems whose solutions would lead to the furthering of disciplines in mathematics. As such, some were areas for investigation and therefore not strictly "problems." 1a. Is there a transfinite number between that of a

17. Unsolved Problems Including the list of 50 problems of Bondy and Murty with current status. Compiled by Stephen C. Locke. 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. Bojan Mohar lists some additional graph theoretic problems. The reconstruction conjecture . (S.M. Ulam, 1960) 2. A graph

18. Open Problems List A collection of papers outlining unsolved problems maintained at Stony Brook. 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

19. Mathematical Problems By David Hilbert Take any definite unsolved problem, such as the question as to the irrationality of 33 D. Hilbert Ueber die Theorie der algebraischen Formen, math. http://aleph0.clarku.edu/~djoyce/hilbert/problems.html

Mathematical Problems Lecture delivered before the International Congress of Mathematicians at Paris in 1900 By Professor David Hilbert Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose? History teaches the continuity of the development of science. We know that every age has its own problems, which the following age either solves or casts aside as profitless and replaces by new ones. If we would obtain an idea of the probable development of mathematical knowledge in the immediate future, we must let the unsettled questions pass before our minds and look over the problems which the science of today sets and whose solution we expect from the future. To such a review of problems the present day, lying at the meeting of the centuries, seems to me well adapted. For the close of a great epoch not only invites us to look back into the past but also directs our thoughts to the unknown future. 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. As long as a branch of science offers an abundance of problems, so long is it alive; a lack of problems foreshadows extinction or the cessation of independent development. Just as every human undertaking pursues certain objects, so also mathematical research requires its problems. It is by the solution of problems that the investigator tests the temper of his steel; he finds new methods and new outlooks, and gains a wider and freer horizon.

20. Unsolved Problems Several people have asked me about unsolved problems. I will take the easy wayout see FP Ramsey. On a problem in formal logic. Proc. London math. Soc. 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. Bojan Mohar lists some additional graph theoretic problems. The reconstruction conjecture . (S.M. Ulam, 1960) 2. A graph

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