Short description:

I have never encountered a book of this kind.  The best description of it I can give is that it is a mystery novel? I found it hard to stop reading before I finished (in two days) the whole text. Soifer engages the reader's attention not only mathematically, but emotionally and esthetically.  May you enjoy the book as much as I did!

?Branko Grünbaum

University of Washington

You are doing great service to the community by taking care of the past, so the things are better understood in the future.

?Stanislaw P. Radziszowski, Rochester Institute of Technology

 They [Van der Waerden?s sections] meet the highest standards of historical scholarship.

?Charles C. Gillispie, Princeton University

You have dug up a great deal of information ? my compliments!

?Dirk van Dalen, Utrecht University

I have just finished reading your (second) article "in search of van der Waerden". It is a masterpiece, I could not stop reading it... Congratulations!

?Janos Pach, Courant Institute of Mathematics

"Mathematical Coloring Book" will (we can hope) have a great and salutary influence on all writing on mathematics in the future.? 

?Peter D. Johnson Jr., Auburn University

Just now a postman came to the door with a copy of the masterpiece of the century. I thank you and the mathematics community should thank you for years to come. You have set a standard for writing about mathematics and mathematicians that will be hard to match.

?Harold W. Kuhn, Princeton University

The beautiful and unique Mathematical coloring book of Alexander Soifer is another case of ``good mathematics''? and presenting mathematics as both a science and an art? It is difficult to explain how much beautiful and good mathematics is included and how much wisdom about life is given.

?Peter Mihók, Mathematical Reviews

Long description:

This is a unique type of book; at least, I have never encountered a book of this kind. The best description of it I can give is that it is a mystery novel, developing on three levels, and imbued with both educational and philosophical/moral issues. If this summary description does not help understanding the particular character and allure of the book, possibly a more detailed explanation will be found useful. One of the primary goals of the author is to interest readers?in particular, young mathematiciansorpossiblypre-mathematicians?inthefascinatingworldofelegant and easily understandable problems, for which no particular mathematical kno- edge is necessary, but which are very far from being easily solved. In fact, the prototype of such problems is the following: If each point of the plane is to be given a color, how many colors do we need if every two points at unit distance are to receive distinct colors? More than half a century ago it was established that the least number of colorsneeded for such a coloring is either 4, or 5, or 6 or 7. Well, which is it? Despite efforts by a legion of very bright people?many of whom developed whole branches of mathematics and solved problems that seemed much harder?not a single advance towards the answer has been made. This mystery, and scores of other similarly simple questions, form one level of mysteries explored. In doing this, the author presents a whole lot of attractive results in an engaging way, and with increasing level of depth.

From the reviews:

"It contains a range of combinatorial colouring problems, while those interested in the recent history or the sociology of mathematics will be entertained by lively accounts of the combinatorialists who created and worked on them. ? The book is generally well written and presented, with good diagrams and layout ? . a useful and engaging book." (Robin Wilson, LMS Newsletter, November, 2009)

?This book contains much math of interest and pointers to more math of interest. ? This is a Fantastic Book!. ? The upward closure of the union of the following people: (1) an excellent high school student, (2) a very good college math major, (3) a good grad student in math or math-related field, (4) a fair PhD in combinatories, or (5) a bad math professor. ? Anyone who is interested in math or history of math. This book has plenty of both.? (William Gasarch, SIGACT News, Vol. 40 (3), 2010)

?Soifer does a fine job in collating a huge range of sources ? with manyinteresting nuggets and, where necessary, a real determination to set the historical record straight in terms of the appellation of conjectures and theorems. ? The mathematical colouring book is attractively produced and very readable. ? book is likely to be of primary interest to those seeking a historically aware, up-to-date introductory survey of an engaging, and still emerging, field of combinatorial mathematics.? (Nick Lord, The Mathematical Gazette, Vol. 95 (532), March, 2011)

?This very nicely presented book, lovingly prepared by the author over a period of 18 years, studies problems involving colored objects, and the Ramsey theory that such problems are imbedded into. ? recommend this book, both for mathematicians and for those who wish to learn more about mathematicians and their subject.? (Arthur T. White, Zentralblatt MATH, Vol. 1221, 2011)

Table of Contents:

Merry-Go-Round.- A Story of Colored Polygons and Arithmetic Progressions.- Colored Plane.- Chromatic Number of the Plane: The Problem.- Chromatic Number of the Plane: An Historical Essay.- Polychromatic Number of the Plane and Results Near the Lower Bound.- De Bruijn?Erd?s Reduction to Finite Sets and Results Near the Lower Bound.- Polychromatic Number of the Plane and Results Near the Upper Bound.- Continuum of 6-Colorings of the Plane.- Chromatic Number of the Plane in Special Circumstances.- Measurable Chromatic Number of the Plane.- Coloring in Space.- Rational Coloring.- Coloring Graphs.- Chromatic Number of a Graph.- Dimension of a Graph.- Embedding 4-Chromatic Graphs in the Plane.- Embedding World Records.- Edge Chromatic Number of a Graph.- Carsten Thomassen?s 7-Color Theorem.- Coloring Maps.- How the Four-Color Conjecture Was Born.- Victorian Comedy of Errors and Colorful Progress.- Kempe?Heawood?s Five-Color Theorem and Tait?s Equivalence.- The Four-Color Theorem.- The GreatDebate.- How Does One Color Infinite Maps? A Bagatelle.- Chromatic Number of the Plane Meets Map Coloring: Townsend?Woodall?s 5-Color Theorem.- Colored Graphs.- Paul Erd?s.- De Bruijn?Erd?s?s Theorem and Its History.- Edge Colored Graphs: Ramsey and Folkman Numbers.- The Ramsey Principle.- From Pigeonhole Principle to Ramsey Principle.- The Happy End Problem.- The Man behind the Theory: Frank Plumpton Ramsey.- Colored Integers: Ramsey Theory Before Ramsey and Its AfterMath.- Ramsey Theory Before Ramsey: Hilbert?s Theorem.- Ramsey Theory Before Ramsey: Schur?s Coloring Solution of a Colored Problem and Its Generalizations.- Ramsey Theory before Ramsey: Van der Waerden Tells the Story of Creation.- Whose Conjecture Did Van der Waerden Prove? Two Lives Between Two Wars: Issai Schur and Pierre Joseph Henry Baudet.- Monochromatic Arithmetic Progressions: Life After Van der Waerden.- In Search of Van der Waerden: The Early Years.- In Search of Van der Waerden: The Nazi Leipzig, 1933?1945.- In Search of Van der Waerden: The Postwar Amsterdam, 1945166.- In Search of Van der Waerden: The Unsettling Years, 1946?1951.- Colored Polygons: Euclidean Ramsey Theory.- Monochromatic Polygons in a 2-Colored Plane.- 3-Colored Plane, 2-Colored Space, and Ramsey Sets.- Gallai?s Theorem.- Colored Integers in Service of Chromatic Number of the Plane: How O?Donnell Unified Ramsey Theory and No One Noticed.- Application of Baudet?Schur?Van der Waerden.- Application of Bergelson?Leibman?s and Mordell?Faltings? Theorems.- Solution of an Erd?s Problem: O?Donnell?s Theorem.- Predicting the Future.- What If We Had No Choice?.- A Glimpse into the Future: Chromatic Number of the Plane, Theorems and Conjectures.- Imagining the Real, Realizing the Imaginary.- Farewell to the Reader.- Two Celebrated Problems.