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         Math Unsolved Problems:     more detail
  1. Tomorrow's Math: Unsolved Problems for the Amateur by Charles Stanley Ogilvy, 1972-02
  2. Tomorrow's Math: Unsolved Problems for the Amateur
  3. Math Odyssey 2000: Puzzles, Mysteries, Unsolved Problems, Breakthroughs, and the People of Mathematics by Clement W. Falbo, 1994-01
  4. Tomorrows Math 2ND Edition Unsolved Problems Fro by C Stanley Ogilvy, 1972
  5. Unsolved Problems of Noise and Fluctuations: UPoN'99: Second International Conference, Adelaide, Australia 11-15 July 1999 (AIP Conference Proceedings)
  6. Math Odyssey Two Thousand ,Puzzles, Mysteries, Unsolved Problems, Breakthroughs, &the People of Mathematics 1994 publication by ClementW.Falbo, 1994-01-01
  7. Old and New Unsolved Problems in Plane Geometry and Number Theory (Dolciani Math by Victor Klee; Stan Wagon, 1996-01-01

21. Math Forum - Ask Dr. Math
Unsolvable and unsolved problems. Date 02/19/98 at 181657 From DJitsu Subject11th Grade Research Paper Dear Dr. math, I need help getting started on a
http://mathforum.org/library/drmath/view/52540.html

Associated Topics
Dr. Math Home Search Dr. Math
Unsolvable and Unsolved Problems
Date: 02/19/98 at 18:16:57 From: D-Jitsu Subject: 11th Grade Research Paper Dear Dr. Math, I need help getting started on a research paper, as well as on doing the project. The topic of my report is "The Impossible and Unsolved in Mathematics (Goldbach's Conjecture, Squaring the Circle, etc.). I was just wondering if I could get some references, tips, or ideas on how to get started. This is for a pre-calculus class. http://ug.cs.dal.ca/~campbell/colllink.html http://mathforum.org/dr.math/ Associated Topics
High School History/Biography

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22. About "Unsolved Problems In Function Theory"
unsolved problems in Function Theory. Library Home Full Table of Contents Suggest a Link Library Help Visit this site http//www.math.purdue.edu
http://mathforum.org/library/view/16365.html
Unsolved Problems in Function Theory
Library Home
Full Table of Contents Suggest a Link Library Help
Visit this site: http://www.math.purdue.edu/~eremenko/uns.html Author: Alexandre Eremenko Description: Files available in PDF format: Some constants studied by Littlewood; Meromorphic functions satisfying certain differential equations (E. Hille); Does every universe contain a place where you can stay at rest? (Lee Rubel); Holomorphic curves with few inflection points; Exceptional set in Gross' Theorem; Modified Cartan's Conjecture. Levels: College Research Languages: English Resource Types: Problems/Puzzles Math Topics: Functional Analysis
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webmaster@mathforum.org

23. Deniz Yuret - Math > Unsolved
unsolved Home math unsolved. These are the 24 problems from the wonderful book Old and new unsolved problems in plane geometry and number theory by Victor
http://home.ku.edu.tr/~dyuret/math/unsolved.html
Unsolved
Home
Math These are the 24 problems from the wonderful book "Old and new unsolved problems in plane geometry and number theory" by Victor Klee and Stan Wagon, MAA, 1991. Some problems are too cryptic to understand without the book. I'll type more explanations some day. Plane Geometry
  • Is each reflecting polygonal region illuminable?
    (Imagine a room in a 2-D universe. If the walls form a polygonal shape and they reflect light, can you always illuminate the whole room with a single light source?)
  • A point P inside a closed convex curve C is called equichordal if every chord of C drawn through point P has the same length. Is there a curve with two equichordal points?
    (Marek Rychlik kindly informed me of his solution to this problem. His homepage has references for the published work.)
  • When congruent disks are pushed closer together, can the area of their union increase?
  • If a convex body C contains a translate of each plane set of unit diameter, how small can C's area be?
  • What is the smallest number f(n) such that any set of f(n) points (non-collinear) always contains the vertices of some convex n-gon?
  • If n points are not collinear, must one of them lie on at least n/3 connecting lines?
  • 24. Deniz Yuret - Math
    unsolved Old and new unsolved problems in plane geometry and number theory Theseare the problems from the MAA Related links A collection of math links.
    http://home.ku.edu.tr/~dyuret/math/
    Deniz Yuret's Math Problems
    Home
    Please mail any interesting problems you find to deniz.yuret@alum.mit.edu . I cited the people I heard the problems from, they are not necessarily the originators. The unsolved flag just means that the problem is yet unsolved by me. Send me a solution if you find one.
    Problems
    This is a list of elementary problems I like for one reason or another from various branches of mathematics.
    Probability twisters
    Click here for a number of problems that will puzzle your probabilistic intuition. These are my favorites. Choose between several different arguments that lead to different answers for each problem.
    Unsolved
    Old and new unsolved problems in plane geometry and number theory: These are the problems from the MAA book by Victor Klee and Stan Wagon (1991).
    Related links
    A collection of math links.
    Sun Jan 12 13:05:39 EET 2003

    25. Math Education: Newsletter: MFIN 2.22, MathPro Unsolved Problems URL Change
    Hi . Tony Thrall very kindly points out that the URL given in this week's MathForum Internet News for the MathPro unsolved problems archive breaks.
    http://www.math.yorku.ca/Who/Faculty/Monette/MathEd/0011.html
    Newsletter: MFIN 2.22, MathPro Unsolved Problems URL change
    Sarah Seastone ( sarah@forum.swarthmore.edu
    Sat, 31 May 1997 22:28:40 -0400 (EDT)
    Hi -
    Tony Thrall very kindly points out that the URL given in this week's Math
    Forum Internet News for the MathPro Unsolved Problems archive breaks.
    MathPro seems to have updated its site this week and I didn't re-check the
    URL before I e-mailed the newsletter. I should know better. Here's the
    updated information:
    (2) UNSOLVED PROBLEM OF THE WEEK ARCHIVE - MATHPRO PRESS
    http://www.mathpro.com/math/puzzles/unsolvedMathProblems/archive.html

    Postings of some difficult yet interesting problems that
    mathematicians are investigating, with references to more information about the topics. http://www.mathpro.com/math/puzzles/unsolvedMathProblems/references.html Although these problems can be understood by the average person, mathematicians have been unsuccessfully working

    26. Math Education: Newsletter: Math Forum Internet News No. 2.22 (June 2)
    MathPro unsolved problems URL change ; Previous message Sarah Seastone NewsletterMath Forum Internet News, No. 2.19 (May 12) . 2 June 1997 Vol.2, No.22.
    http://www.math.yorku.ca/Who/Faculty/Monette/MathEd/0010.html
    Newsletter: Math Forum Internet News No. 2.22 (June 2)
    Sarah Seastone ( sarah@forum.swarthmore.edu
    Sat, 31 May 1997 19:23:29 -0400 (EDT)
    2 June 1997 Vol.2, No.22
    THE MATH FORUM INTERNET NEWS
    From the CONNECTED CURRICULUM PROJECT
    MATHEMATICAL MODELING IN A REAL AND COMPLEX WORLD
    by Frank Wattenberg
    http://ascc.carroll.edu/ccp/modeling/topic.htm

    "Among the first customers for a new car are engineers
    from competing companies. They need to know what their
    competition is doing and how. One of the most important
    tools for figuring out how a competitor's product works is reverse engineering. Engineers have a general idea of the tools used by their competitors and they can use their own ideas to try to reconstruct what competing engineers have done. This course is about modeling, or reverse

    27. My Favorite Open Problems
    unsolved problems from Bondy and Murty. see my math links page forlinks to other sites with unsolved problems. Back to my homepage.
    http://www.math.princeton.edu/~matdevos/open/open.html
    Open Problems in Discrete Math
    Prizes
    Flows on Graphs
    Cycle Covers
    Choosability for Ax=y
    Edge Coloring
    Vertex Coloring
    Directed Graphs
    Topological Graph Theory
    Matroid Theory
    Additive Number Theory
    Miscellaneous Problems

    please feel free to email me if you know of unmentioned progress (possibly a solution) to any of these problems.

    28. Sci.math FAQ: Unsolved Problems
    Vorherige Nächste Index sci.math FAQ unsolved problems. Subject sci.mathFAQ unsolved problems; From alopezo@neumann.uwaterloo.ca (Alex Lopez-Ortiz);
    http://www.uni-giessen.de/faq/archiv/sci-math-faq.unsolvedproblems/msg00000.html
    Index
    sci.math FAQ: Unsolved Problems

    29. Mathematical Problems
    In various subjects, compiled by Torsten Sillke.Category Science math Research Open problems...... or the diameter of GL(n,F2); Combinatorial Games unsolved problems (by RK OftenShould You Beat Your Kids; Expectation Linearity - problems solved by math-News.
    http://www.mathematik.uni-bielefeld.de/~sillke/problems.html
    Mathematical Problems
    Graph Theory
    Number Theory
    Combinatorics

    30. NZ
    problems. mathFAQ) The Hilbert ~ (from the math-FAQ) mathematics of Knots (elementary)The trisection of an angle (from the math-FAQ) unsolved ~ (from the
    http://cage.rug.ac.be/~hvernaev/catN-Z.html
    The Math Catalog: N-Z
    A-M N-Z
    Newsgroups
    sci.math
    sci.math.num-analysis
    sci.math.research
    sci.math.symbolic
    Nonstandard Analysis
    Homepages of Nonstandard Analysis People (a local version is behind this button)
    Number Theory
    Some Web-sources Prime Numbers:
  • from the Math-FAQ
  • Caldwell's List of the Largest ~
  • Primality tests (a local version is behind this button)
  • Mersenne-primes (a local version is behind this button)
  • Short history
  • (elementary introduction to number theory) Fermat's Last Theorem (FLT):
  • from the Math-FAQ
  • from the University of St Andrews
  • a (Dutch) newspaper-article
  • a DVI-file : introduction to FLT Probability of 2 numbers being coprime
    Fibonacci numbers and the Golden Section
    Olympiads
    International Mathematical Olympiad
    IMO-problems (1959 - now)
    International Mathematical Olympiad 1993-96
    Dutch IMO-site (with info about other Math Olympiads, too)
    Math competitions archive
    Math problems archive
    Argentina Math Olympiad
    Bulgarian Math Olympiad ...
    Estonian Math Olympiad (Estonian)
    Flanders Math Olympiad (VWO)
    Iberoamerican Math Olympiad (Spanish)
    Irish Math Olympiad
    Italian Math Olympiad (Italian)
    Mexican Math Olympiad (Spanish)
    Dutch Math Olympiad
    Norwegian Math Olympiad (`Niels Henrik Abels matematikk-konkurranse')
    Polish Math Olympiad
    Romanian Math Olympiad
    Singaporean IMO-team
    South-African IMO-team ...
    Russian Math Olympiad
    An excerpt from questions (mostly) from the Dutch Math Olympiad (Dutch)
    See also: Contests
    Organisations
    A list of ~
    American Mathematical Society (AMS)
    Canadian Mathematical Electronic Services (Camel)
  • 31. F. Conjectures (Math 413, Number Theory)
    A collection of easily stated conjectures which are still open. Each conjecture is stated along with Category Science math Number Theory Open problems......F. Conjectures. Number Theory, math 413, Fall 1998. Refs unsolved problems, Klee Wagon, 1991, Sect 17; Elementary Number Theory, Jones Jones, 1998, Chap 9;
    http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html
    F. Conjectures
    Number Theory, Math 413, Fall 1998
    A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references.
  • The Riemann Hypothesis Fermat Numbers Goldbach's Conjecture Catalan's Conjecture ... The Collatz Problem
  • The Riemann Hypothesis
    Def: Riemann's Zeta function, Z(s), is defined as the analytic extension of sum n infty n s Thm: Z( s )=prod i infty p i s , where p i is the i th prime. Conj: The only zeros of Z( s ) are at s s Thm: The Riemann Conjecture is equivalent to the conjecture that for some constant c x )-li( x c sqrt( x )ln( x where pi( x ) is the prime counting function.
    Def: n is perfect if it is equal to the sum of its divisors (except itself). Examples are 6=1+2+3, 28, 496, 8128, ... Def: The n th Mersenne Number, M n , is defined by M n n Thm:
    • M n is prime implies that n n is perfect. (Euclid)

    32. Unsolved Problems
    Hi! We're E and Pi, here to introduce you to Jon Bettencourt's webpage on unsolved math problems. It's his final project for COSMOS
    http://www.geocities.com/jonrelay/cosmos/
    Hi! We're E and Pi, here to introduce you to Jon Bettencourt's web page on unsolved math problems. It's his final project for COSMOS, the math and science program he's in. Is he going to be surprised when he sees what we've done!
    Our favorite problem is the one about e (pi* n) being close to integers, since it involves us! Although Pi says she likes the formula for any digit of pi better (of course).
    To which Jon responds... I'm gonna get them for this! If E and Pi keep messing with this page, I'll have to get Bromine to get them off my back, and I know they don't want that!
    More information on E and Pi
    (the characters, not the numbers)
    Anyway, I have been gathering information on unsolved problems from the Internet and other sources. Here are a few of the problems I have found and some information on some of them.
    Some of these problems seem very simple, but end up with no simple proof or solution to them. As an example, Fermat's Last Theorem was very simple, but it took hundreds of years and some parts from very advanced branches of mathematics to solve it. So if one seems simple, don't try to solve it unless you know a lot of math.
    More information about unsolved problems can be found with a search for unsolved problems on Google.com

    33. Maine Math Talent Search : Math Links
    unsolved problems; Meeroh's math problems; Interactive problems; mathOracle; math contests; unsolved math problems; math olympiad; Ask
    http://www.geocities.com/CollegePark/Center/1539/p89.htm
    Math Education
  • A must site for teachers
  • MegaMathematics K-12 fun room
  • Links to math education
  • Links to great math topics ...
  • Digital education on the net Computers and Mathematics
  • Waterloo Maple software
  • Symbolic computation
  • Math software
  • Math online ...
  • Mathematics on the internet Problem Solving
  • Famous problems
  • Alphametrics
  • Word problems for kids
  • Online math problems ...
  • Solving word problems History, Foundations, Logic
  • History of mathematics
  • Zermelo-Fraenkel axioms
  • Goedel's theorem (hyper-textbook)
  • Liar's paradox ...
  • Notable women in mathematics Applied Mathematics
  • Math in technology?
  • Minnesota Research Associates
  • Dynamics and complex variables
  • Mathematics/Genome Project ...
  • Mathematics and artificial intelligence General Math Links
  • Math Net
  • Math search
  • Math organizations
  • Cornell math gateway ...
  • Canadian mathematical society Miscellaneous
  • Jobs in mathematics
  • The abacus
  • Careers in mathematics
  • Works of great mathematicians ...
  • Interactive statistics Algebra, Number Theory
  • Abstract algebra
  • Continued fractions
  • Prime number research
  • Fun with numbers ...
  • Algebraic number theory Geometry, Topology
  • Geometry and topology examples
  • Applications of Geometry
  • Oswald Veblen
  • Euler's formula ...
  • Geometry and geneology Univ of Maine Math Courses
  • General Service Courses
  • Analysis
  • Statistics
  • Logic, Foundations, History
  • 34. MATH-abundance
    More than 400 math problems in 1 file unsolved math problems. InternetCenter for mathematics problems. Many other math links. mathematics
    http://www.jct.ac.il/science/math/MathAbundance/
    MATH-abundance

    35. Mathematical Problems - Problem Solving - Mathematical Competitions (Math Links
    mathematics Hots (problems) by Bruno KeviusCategory Science math Recreations...... by subtracting squares (Dean Hickerson and Michael Kleber); Shack's math problemsby Michael Shackleford, ASA; unsolved mathematics problems mathsoft; unsolved
    http://www.abc.se/~m9847/matre/problem.html
    Mathematical Resources
    Math Links by Bruno Kevius
    This list is continually under development
    Mathematical Problems - Problem Solving
    Mathematical Competitions
    not a complete list, only what I happened to see...

    36. Unsolved Math Problems
    unsolved math problems unsolved mathematics problems mathsoft providesan archive of unsolved math problems plus links to related sites.
    http://westford.mec.edu/schools/tips/unsolved.htm
    Unsolved Math Problems
    Unsolved Mathematics Problems

    Mathsoft provides an archive of unsolved math problems plus links to related sites.
    http://www.mathsoft.com/asolve/index.html There are really impossible things ...
    This site includes slider puzzles as well as many other mind-numbing puzzles.
    http://www.cut-the-knot.com/impossible/index.html CICA Project Fermat
    The animation presents a popularized introduction to Fermat's Last Theorem. Three dimensional mathematical depictions are used in the beginning of the film to illustrate the meaning of the mathematical ideas involved. The second half of the film makes a transition to show a remarkable family of four dimensional surfaces related to Fermat's theorem, and projects them to three dimensions for display using standard rendering and shading techniques.
    http://www.cica.indiana.edu/projects/Fermat/index.html Unsolved Problems
    Here you'll find Goldbach's and Collatz's conjectures and the number of twin primes.
    http://abel.math.umu.se/~frankw/unsolved.html

    37. Unsolved Problems
    References. unsolved problems in Number Theory. Richard K Guy. Springer, ProblemE16. GT Leavens and M. Vermeulen 3x+1 search programs Comput. math. Appl.
    http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node30.html
    Next: Mathematical Games Up: Famous Problems in Mathematics Previous: Which are the 23
    Unsolved Problems
    Does there exist a number that is perfect and odd?
    A given number is perfect if it is equal to the sum of all its proper divisors. This question was first posed by Euclid in ancient Greece. This question is still open. Euler proved that if N is an odd perfect number, then in the prime power decomposition of N , exactly one exponent is congruent to 1 mod 4 and all the other exponents are even. Furthermore, the prime occurring to an odd power must itself be congruent to 1 mod 4. A sketch of the proof appears in Exercise 87, page 203 of Underwood Dudley's Elementary Number Theory. It has been shown that there are no odd perfect numbers
    Collatz Problem
    Take any natural number
    n : = m;
    repeat
    n is odd) then n : = 3*n + 1 ; else n : = n/2
    until ( n==1
    Conjecture 1. For all positive integers m, the program above terminates. The conjecture has been verified for all numbers up to References Unsolved Problems in Number Theory.

    38. Unsolved Problems
    next up previous contents Next Does there exist a Up Famous problemsin Mathematics Previous Which are the. unsolved problems.
    http://db.uwaterloo.ca/~alopez-o/math-faq/node59.html
    Next: Does there exist a Up: Famous Problems in Mathematics Previous: Which are the
    Unsolved Problems

    Alex Lopez-Ortiz
    Mon Feb 23 16:26:48 EST 1998

    39. The State News - Www.statenews.com
    Leonard Ford at Wells Hall. math problems left unsolved By LESLIE ESCOBARThe State News. When journalism freshman Marshall Weinbaum
    http://www.statenews.com/article.phtml?pk=7165

    40. Math Digest
    This article concerns the legacy of unsolved problems that Erdos leftbehind and the cash prizes associated with those problems.
    http://www.ams.org/new-in-math/mathdigest/200205-erdos.html
    Mathematical Digest
    Short Summaries of Articles about Mathematics
    in the Popular Press
    "Erdos's Hard-To-Win Prizes Still Draw Bounty Hunters," by Charles Seife. Science, 5 April 2002, pages 39-40. Paul Erdos, with an output of more than 1500 papers during his lifetime, has had 62 papers bearing his name published since his death. This article concerns the legacy of unsolved problems that Erdos left behind and the cash prizes associated with those problems. People who solve a problem receive a cash award, the size of which depends on the difficulty of the problem. In 1993, Ron Graham had Erdos sign some of Graham's checks "to be filled out later." These checks are intended as souvenirs for those who solve a problem, but Graham also sends out real checks (bearing his signature). He has sent out about $3000 so far and estimates that the remainder of the unsolved problems have awards totalling about $25,000. The article concludes with a quote from Graham regarding Erdos' unsolved problems: "These problems serve as Socratic gadflies, reminding us of how much we have to learn." - Mike Breen

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