MathSoft Unsolved Problems

Steven Finch, MathSoft Engineering & Education, Inc.

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.

Some of the essays contain links to Mathcad files. If you don't own Mathcad, please consider downloading the free read-only version called Mathcad Explorer.

I will be happy to consider your submissions for publication (e-address here), in either the form of HTML or Mathcad files. Please ensure that the references page for your submission is as complete as possible (simply because this is helpful to readers who attempt to solve your problems). I would also appreciate notifications of relevant web links.

Unsolved Problems on the MathSoft Site

MathSoft Constants (there are many constants in mathematics other than and e)
The Miraculous Bailey-Borwein-Plouffe Pi Algorithm (quadrillionth binary digit of now known)
On a Generalized Fermat-Wiles Equation (full Taniyama-Shimura conjecture apparently proved)
Zero Divisor Structure in Real Algebras (partial solution by Michael Schweitzer)
Sleeping Habits of Armadillos (contributed by Larry Glasser)
Questions Involving the Smarandache Function
Moat Crossing Optimization Problem
Linear Independence of Exponential Functions (contributed by Sherman Stein)
Large Sets Missing Many Circles (contributed by George Baloglou and Phil Tracy)
Operator Norms of Complex Matrices (contibuted by Zdislav Kovarik)

Links to Other Sites

Clay Mathematics Institute Millennium Prize Problems
Jeff Lagarias' 3x+1 problem and related problems (AT&T; Labs Research); also Keith Matthew's The Generalized 3x+1 Mapping (University of Queensland) and 1999 Conference on the Collatz Problem Proceedings (Eichstätt, Germany)
Alex Lopez-Ortiz's sci.math FAQ on Famous Problems in Mathematics (University of New Brunswick)
Nils Bruin's Generalization of the ABC-Conjecture (Leiden University, The Netherlands)
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), Andrea Ercolino's XGC page and Jeffrey Gold's Characterization of Twin Prime Pairs; also Goldbach's Conjecture - Recent Progress and Waring's Problem - Hard Part.
David Moews' Perfect, Amicable and Sociable Numbers (University of Connecticut), Jan Otto Munch Pedersen's Known Amicable Pairs (Vejle Business College, Denmark) and Chris Caldwell's Mersenne Primes: History, Theorems and Lists (University of Tennessee at Martin)
Lost in a Forest (Algorithms Project, INRIA Rocquencourt)
Richard Weber's Unsolved Problems in Operations Research (University of Cambridge)
MegaMath Open Problems (Los Alamos and University of Idaho)
M. Beeler, R. W. Gosper and R. Schroeppel's Hakmem collection, MIT AI Memo 239
David Eppstein's Open Problems from the Geometry Junkyard (University of California at Irvine)
Richard K. Guy's Unsolved Problems in Combinatorial Game Theory (Gustavus Adolphus College)
Jeff Erickson's Open Problems; also listing of problems from AMS conference "Discrete and Computational Geometry: Ten Years Later" (Duke University)
Kevin Brown's Most Wanted List
Ulam s-Additive Sequences and Several Problems Concerning Sum-Free Sets (Algorithms Project, INRIA Rocquencourt)
Questions in Topology (Topology Atlas)
Frank Wikström's Some Unsolved Problems with Elementary Formulation (Umeå University)
Franz Lemmermeyer's Unsolved Problems in Algebraic Number Theory (University of Heidelberg) - in postscript
Dave Rusin's Mathematical Atlas (Northern Illinois University) - do keyword search on "open"
Ulam Quarterly Electronic Scottish Café (University of Southern Mississippi) - do keyword search on "open"
C. D. Godsil's Problems in Algebraic Combinatorics, from the Electronic Journal of Combinatorics (Georgia Institute of Technology); William Martin's Open Problems (University of Winnipeg) overlaps with this somewhat
Mike Keith's Mathematical Diversions
Eugenio Calabi's Circumscribing Tetrahedron of Least Volume (Algorithms Project, INRIA Rocquencourt)
André Kézdy's Open Problems - Partitioning Permutations (University of Louisville)
Open Problems from Constructive Approximation - P. Borwein, I. Daubechies and V. Totik (Simon Fraser University)
Cristian Calude's Algorithmic Information Theory: Open Problems (University of Auckland, New Zealand)
Douglas Zare's Open Problems (California Institute of Technology)
Day Kirby's E4K Gallery Of Open Problems, part of Mathmania page (University of Victoria)
Three Quadratic Recurrences and Powers of 3/2 Modulo One (Algorithms Project, INRIA Rocquencourt)
Open Problems in Dynamical Systems, including several complex variables and low-dimensional topology (SUNY at Stony Brook)
Frank Ruskey's Open problems related to Venn diagrams, part of The Venn Diagram Page (University of Victoria).
Darrin Speegle's Open Problems in Linear Analysis and Probability (Texas A&M; University)
Quentin F. Stout's Some Open Problems and Conjectures about Graph Theory (University of Michigan)
Naoki Sato's Unsolved Problems (Yale University)
Michael Brundage's Unsolved Problems about Graceful Graphs (California Institute of Technology)
Jorge Urrutia's Open Problems on Discrete and Computational Geometry (University of Ottawa)
Triangulating an n-Dimensional Cube (Algorithms Project, INRIA Rocquencourt)
James Currie's Words Avoiding Patterns (University of Winnipeg)
Phil Gibbs' 1, 3, 8, 120 - do there exist five positive integers such that the product of any two is one less than a square? - see also Kevin Brown's If ab+1, ac+1, bc+1 are squares
Palindrome Conjecture, discussed in Kevin Brown's Digit Reversal Sums Leading to Palindromes, John Walker's Three Years Of Computing, Tim Irvin's About Two Months of Computing, and Dave Rusin's two articles one and two.
Vsevolod Lev's Problems Page (University of Georgia)
Dario Alpern's Table of numbers problem (in both Spanish and English)
Chen Shuwen's Unsolved problems and conjectures regarding Equal Sums of Like Powers; see also Jean-Charles Meyrignac's Computing Minimal Equal Sums Of Like Powers
Bruno Kevius' Mathematical Problems (Vasalundsgymnasiet, Sweden)
Torsten Sillke's Puzzle Results and Problems (Universität Bielefeld, Germany)
Achim Flammenkamp's Own Mathematical Works (Universität Bielefeld, Germany)
A Convex Maximization Problem and Polynomial Optimization Over an Ellipse (Algorithms Project, INRIA Rocquencourt)
James Propp's Enumeration of Matchings: Problems and Progress - see also supplementary progress report (Univ. of Wisconsin)
Gordon Royle's Open Questions in Combinatorics (University of Western Australia)
Brian Almond's The Wedge: Distinct Elements in Arithmetic Tables
Robert Hochberg's Open Problems for Undergraduates (DIMACS)
Mok-Kong Shen's Two Mathematical Problems (Ludwig-Maximilians-University Munich)
Rob Kirby's Unsolved Problems in Low-Dimensional Topology (University of California, Berkeley)
Mladen Bestvina's Geometric Group Theory Problem List (University of Utah)
Theodore Salman's Open Questions in Recursion Theory (University of California, Berkeley)
Lonely Runner Conjecture; link to Bienia, Goddyn, Gvozdjak, Sebö & Tarsi's Flows, view-obstructions, and the lonely runner and Goddyn & Wong's Tight Instances of the lonely runner
Pavel Emelianov's Snake-in-the-Box Problem (Ecole Polytechnique)
Philippe Flajolet and Helmut Prodinger's Problems in Analysis of Algorithms (Algorithms Project, INRIA Rocquencourt)
Peter Cameron's Old Homepage Problems and Problems on Permutation Groups (Queen Mary & Westfield College)
Sums of Binomial Coefficients and Power Sums of Complex Numbers (Algorithms Project, INRIA Rocquencourt)
Fan Chung Graham's Open problems of Paul Erdös in Graph Theory (University of Pennsylvania); also J. Graph Theory 25 (1997), 3-36
Stephen C. Locke's Unsolved Problems in Graph Theory (Florida Atlantic University)
Thomas Zaslavsky's Problems in Signed, Gain, and Biased Graphs and Problems in Matroid Theory (Binghamton University of SUNY)
Dan Archdeacon's Problems in Topological Graph Theory (University of Vermont)
Marion Scheepers' The Boise Problem Book (Boise State University)
Open Problems in Combinatorial Group Theory (New York Group Theory Cooperative)
Random Binary Trees Grown via the Galton-Watson Branching Process (Algorithms Project, INRIA Rocquencourt)
Douglas West's Open Problems in Discrete Mathematics (University of Illinois in Urbana/Champaign)
Nathaniel Dean's Open Problems in Graph Minors (Rice University)
Jerry Spinrad's Open Problems in Graph Algorithms (Vanderbilt University)
Siemion Fajtlowicz and Ermelinda DeLaVina's Conjectures Produced by the Program Graffiti (University of Houston)
Joe Ganley's Open Problems in Steiner Trees
Roy Williams' Exp(Pi*Sqrt(n)) Page (Calif.Instit. of Technology)
Clark Kimberling's Unsolved Problems and Rewards (University of Evansville)
Andreas Gammel's Self-Avoiding Walks of a Rook on a Chessboard (Algorithms Project, INRIA Rocquencourt)
Alexandre Eremenko's Favorite unsolved problems (Purdue University)
Tetsuya Hattori's A Nice Theorem Wanted! (Rikkyo University, Japan)
Problem Involving an Integral Equation; see also Hilbert's Moment Problem (University of Toronto)
Yves Gallot's Sierpinski problem and Riesel problem pages, from the Proth Search Site.
Matt DeVos' Open Problems in Discrete Math (Princeton University).
Vasek Chvatal's Open Problems on Perfect Graphs (Rutgers University).