Theorem of the Day

Acknowledgements

Many organisations and people have contributed to this site. I have generally preferred to acknowledge this contribution here rather than clutter up individual theorems.

The value of any mathematical resource is predicated on its accuracy. I owe a great debt to all the people (some of whom are mentioned again below) who have confirmed or improved the fitness-for-purpose of any part of these pages (and to whom no residual errors may be attributed): Louigi Addario-Berry, Emmanuel Amiot, David L. Applegate, John Arhin, R.A. Bailey, Robert F. Bailey, Lowell Beineke, Arthur T. Benjamin, Curtis D. Bennett, Dave Benson, Valérie Berthé, Lev Bregman, Martin Bush, Peter Cameron, David Cariolaro, Melody Chan, Philippe Chassaing, Amanda Chetwynd, James Colliander, Bill Cook, John D. Dixon, Kimmo Eriksson, Tony Forbes, Stephen M. Gaglola III, Julian Gilbey, Edray Herber Goins, Mike Grannell, Terry Griggs, Xiaoyang Gu, Thomas Hales, Jonathan I. Hall, John H. Halton, Michael Hardy, Stephan Hell, Ted Hill, Anthony Hilton, Fred Holroyd, Stephen Huggett, Allyn Jackson, Bill Jackson, Peter Jones, Donald Keedwell, Clark Kimberling, Tony Knapp, Ron Knott, Cheng Yeaw Ku, Robert Lockhart, Jack Lutz, Jiří Matoušek, Thomas Mattman, William McCune, Shawn McMurran, Elvira Mayordomo, Francesca Merola, G. Eric Moorhouse, Frank Morgan, Peter M. Neumann, Olavi Nevanlinna, Florian Pfender, Cheryl Praeger, Jean-Jacques Quisquater, Larry Riddle, Dave Rusin, Carrie Rutherford, Sy Samet, Gary Seitz, David Singmaster, J. Michael Steele, Shaun Stevens, Jim Tattersall, Morwen Thistlethwaite, Andrew Thomason, Helge Tverberg, Rémi Vaillancourt, Petr Vojtěchovský, Bert Wehrfritz, Benjamin Weiss, Dominic Welsh, Robin Wilson, Ruth Williams, Larry Wos, Doron Zeilberger.

Spreadsheet screen shots are from OpenOffice Calc, except where individually acknowledged.

Some pages have photo images whose ownership I have been unable to trace. Apologies for any infrigements and please let me know if you are due any acknowledgement or know of some person or organisation who is:

  Gauss' Law of Quadratic Reciprocity (images of Gauss and Legendre)

  The Merton College Theorem (photos of Merton and Oriel Colleges)

  The Pythagorean Theorem (photo of Edsger Dijkstra)

  Ramsey's Theorem (photo of Paul Erdös)

Particular thanks to:

Latimer Clarke Corporation Pty Ltd, for permission to use a map from Atlapedia to illustrate the Four Colour Theorem.

London South Bank University for hosting the pdf files belonging to the site.

The Math Forum for permission to use their image of Pascal's triangle to illustrate Lucas' Theorem.

Perseus Book Group for permission to quote the dedicatory poem from Harary's Graph Theory in Kuratowski's Theorem.

Robert F. Bailey for permission to use his image of the Biggs-Smith graph to illustrate Cameron's theorem on distance-transitive graphs.

Valérie Berthé for sending me the .pdf version of her survey article with Pascal Alessandri, being the web link from the Three-Distance Theorem.

Peter Cameron for drawing my attention to Babai's 1989 proof of Dixon's conjecture about Netto's conjecture; and to R.A. Bailey's 1984 paper which provided the material for Bailey's Theorem on Latin Squares; for making available the pdf of his short article on parking functions for The Parking Function Formula; and for helpful comments on several other theorems.

Alan Camina for suggesting the Stable Marriage Theorem.

Mike Child for giving me the java to display automatically the current theorem of the day.

Ugo Crépin for suggesting Thales' Theorem.

Tony Forbes for permission to use his jpeg image of consecutive primes in arithmetic progression to illustrate the Green-Tao Theorem; and for providing me with the data necessary to create the image in the Beardwood-Halton-Hammersley Theorem; and for helpful feedback on many other theorems.

Jessica Fridrich for permission to use images of Rubik's cube from her Speed cubing site (check out the video clips of her sub-15-second cubing!) to illustrate Fermat's Little Theorem.

Thomas Hales for patiently correcting my misconceptions about Kepler's Conjecture.

John H. Halton for giving me much help in preparing the Beardwood-Halton-Hammersley Theorem.

Stephen Hell for drawing my attention to the Dutch Cheese Problem, featured in The Tverberg Partition Theorem, which also benefitted from comments by Jiří Matoušek and Tverberg himself.

Allyn Jackson for helping me track down cameo appearances of theorems by pointing me to all sorts of resources about mathematics and the arts.

Donald Keedwell, for alerting me to the fact that the Lagrange Property for Moufang Loops had been proved. And for helpfully checking my presentation of this result.

Clark Kimberling for enlightening me on the history of Zeckendorf's Theorem.

Anthony Knapp has been a generous source of advice on everything from the Cauchy Problem to cohomology (and seems to have written award-winning textbooks or monographs on most of it!)

Ron Knott for helpful comments and suggestions regarding Fibonacci-related theorems, in particular Zeckendorf's Theorem.

Robert Lockhart has made detailed and invaluable comments on many of the theorems.

William McCune for alerting me to the amazingly short single-axiom specification of Boolean Algebra, which appears in the description of The Robbins Problem; and for permission to reproduce part of EQP's solution to that problem.

Justin Mullins for permission to use his art interpretation of Euler's Identity.

Carrie Rutherford for insightful suggestions concerning too many of these theorems to mention individually.

Morwen Thistlethwaite for some informative comments on Reidemeister's Theorem.

Petr Vojtěchovský for drawing my attention to Gagola III and Hall's independent proof of the Lagrange Property for Moufang Loops.

Bert Wehrfritz for helping me to choose and present, as a memorial tribute, Gruenberg's Theorem on Nilpotent Groups.

Dominic Welsh for telling me about the counter-example showing that graphs are not well-quasi-ordered by topological minors (the Robertson-Seymour Graph Minor Theorem).

Jon Woodring for permission to use his ripples graphic to illustrate the First Isomorphism Theorem.