Alexander Soifer (auth.)0387746404, 9780387746401, 0387746404
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
Table of contents :
Front Matter….Pages I-XXX
Front Matter….Pages 1-1
A Story of Colored Polygons and Arithmetic Progressions….Pages 3-9
Front Matter….Pages 11-11
Chromatic Number of the Plane: The Problem….Pages 13-20
Chromatic Number of the Plane: An Historical Essay….Pages 21-31
Polychromatic Number of the Plane and Results Near the Lower Bound….Pages 32-38
De Bruijn–Erdős Reduction to Finite Sets and Results Near the Lower Bound….Pages 39-42
Polychromatic Number of the Plane and Results Near the Upper Bound….Pages 43-49
Continuum of 6-Colorings of the Plane….Pages 50-56
Chromatic Number of the Plane in Special Circumstances….Pages 57-59
Measurable Chromatic Number of the Plane….Pages 60-66
Coloring in Space….Pages 67-71
Rational Coloring….Pages 72-76
Front Matter….Pages 77-77
Chromatic Number of a Graph….Pages 79-87
Dimension of a Graph….Pages 88-98
Embedding 4-Chromatic Graphs in the Plane….Pages 99-109
Embedding World Records….Pages 110-126
Edge Chromatic Number of a Graph….Pages 127-139
Carsten Thomassen’s 7-Color Theorem….Pages 140-144
Front Matter….Pages 145-146
How the Four-Color Conjecture Was Born….Pages 147-162
Victorian Comedy of Errors and Colorful Progress….Pages 163-175
Kempe–Heawood’s Five-Color Theorem and Tait’s Equivalence….Pages 176-186
Front Matter….Pages 145-146
The Four-Color Theorem….Pages 187-194
The Great Debate….Pages 195-206
How Does One Color Infinite Maps? A Bagatelle….Pages 207-208
Chromatic Number of the Plane Meets Map Coloring: Townsend–Woodall’s 5-Color Theorem….Pages 209-223
Front Matter….Pages 225-225
Paul Erdős….Pages 227-235
De Bruijn–Erdős’s Theorem and Its History….Pages 236-241
Edge Colored Graphs: Ramsey and Folkman Numbers….Pages 242-260
Front Matter….Pages 261-261
From Pigeonhole Principle to Ramsey Principle….Pages 263-267
The Happy End Problem….Pages 268-280
The Man behind the Theory: Frank Plumpton Ramsey….Pages 281-296
Front Matter….Pages 297-297
Ramsey Theory Before Ramsey: Hilbert’s Theorem….Pages 299-300
Ramsey Theory Before Ramsey: Schur’s Coloring Solution of a Colored Problem and Its Generalizations….Pages 301-308
Ramsey Theory before Ramsey: Van der Waerden Tells the Story of Creation….Pages 309-319
Whose Conjecture Did Van der Waerden Prove? Two Lives Between Two Wars: Issai Schur and Pierre Joseph Henry Baudet….Pages 320-346
Monochromatic Arithmetic Progressions: Life After Van der Waerden….Pages 347-366
In Search of Van der Waerden: The Early Years….Pages 367-392
In Search of Van der Waerden: The Nazi Leipzig, 1933–1945….Pages 393-417
In Search of Van der Waerden: The Postwar Amsterdam, 1945 166 ….Pages 418-448
In Search of Van der Waerden: The Unsettling Years, 1946–1951….Pages 449-483
Front Matter….Pages 485-485
Monochromatic Polygons in a 2-Colored Plane….Pages 487-499
Front Matter….Pages 485-485
3-Colored Plane, 2-Colored Space, and Ramsey Sets….Pages 500-504
Gallai’s Theorem….Pages 505-518
Front Matter….Pages 519-520
Application of Baudet–Schur–Van der Waerden….Pages 521-524
Application of Bergelson–Leibman’s and Mordell–Faltings’ Theorems….Pages 525-528
Solution of an Erdős Problem: O’Donnell’s Theorem….Pages 529-531
Front Matter….Pages 533-533
What If We Had No Choice?….Pages 535-552
A Glimpse into the Future: Chromatic Number of the Plane, Theorems and Conjectures….Pages 553-556
Imagining the Real, Realizing the Imaginary….Pages 557-563
Front Matter….Pages 565-565
Two Celebrated Problems….Pages 567-568
Back Matter….Pages 569-605
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