About the Book

This book is dedicated to problems involving colored objects, and to results about the existence of certain exciting and unexpected properties that occur regardless of how these objects are colored. In mathematics, these results comprise the beautiful area known as Ramsey Theory. Ramsey Theory includes parts of many fields of mathematics, including combinatorics, geometry, and number theory. This book addresses famous and exciting problems of Ramsey Theory, along with the history surrounding the discovery of Ramsey Theory. In addition, the author studies the life of Issai Schur, Pierre Joseph Henry Baudet and B.L. van der Waerden. Due to the author's correspondence with van der Waerden, Erdös, and Schur, this book contains material that has never before been published. Historians of mathematics will herein find much new information, along with old errors corrected and published here for the first time in book form.

Table of Contents:
Epigraph: To Paint a Bird.- Foreword for the New Mathematical Coloring Book by Peter D. Johnson, Jr.- Foreword for the New Mathematical Coloring Book by Geoffrey Exoo.- Foreword for the New Mathematical Coloring Book by Branko Grunbaum. Foreword for The Mathematical Coloring Book by Peter D. Johnson, Jr., Foreword for The Mathematical Coloring Book by Cecil Rousseau.- Acknowledgements.- Greetings to the Reader 2023.- Greetings to the Reader 2009.- I. Merry-Go-Round.-1. A Story of Colored Polygons and Arithmetic Progressions.- II. Colored Plane.- 2. Chromatic Number of the Plane: The Problem.- 3. Chromatic Number of the Plane: An Historical Essay.- 4. Polychromatic Number of the Plane and Results Near the Lower Bound.- 5. De Bruijn–Erdős Reduction to Finite Sets and Results Near the Lower Bound.- 6. Polychromatic Number of the Plane and Results Near the Upper Bound.- 7. Continuum of 6-Colorings of the Plane.- 8. Chromatic Number of the Plane in Special Circumstances.- 9. MeasurableChromatic Number of the Plane.- 10. Coloring in Space.- 11. Rational Coloring.- III. Coloring Graphs.- 12. Chromatic Number of a Graph.- 13. Dimension of a Graph.- 14. Embedding 4-Chromatic Graphs in the Plane.- 15. Embedding World Series.- 16. Exoo–Ismailescu: The Final Word on Problem 15.4.- 17. Edge Chromatic Number of a Graph.- 18. The Carsten Thomassen 7-Color Theorem.-  IV.Coloring Maps.- 19. How the Four-Color Conjecture Was Born.- 20. Victorian Comedy of Errors and Colorful Progress.- 21. Kempe–Heawood’s Five-Color Theorem and Tait’s Equivalence.- 22. The Four-Color Theorem.- 23. The Great Debate.- 24. How Does One Color Infinite Maps? A Bagatelle.- 25. Chromatic Number of the Plane Meets Map Coloring: The Townsend–Woodall 5-Color Theorem.- V. Colored Graphs.- 26. Paul Erdős.- 27. The De Bruijn–Erdős Theorem and Its History.- 28. Nicolaas Govert de Bruijn.- 29. Edge Colored Graphs: Ramsey and Folkman Numbers.- VI. The Ramsey Principles.- 30. From Pigeonhole Principle to Ramsey Principle.- 31. The Happy End Problem.- 32. The Man behind the Theory: Frank Plumpton Ramsey.- VII. Colored Integers: Ramsey Theory Before Ramsey and Its AfterMath.- 33. Ramsey Theory Before Ramsey: Hilbert’s Theorem.- 34. Ramsey Theory Before Ramsey: Schur’s Coloring Solution of a Colored Problem and Its Generalizations.- 35. Ramsey Theory Before Ramsey: Van der Waerden Tells the Story of Creation.- 36. Whose Conjecture Did Van der Waerden Prove? Two Lives Between Two Wars: Issai Schur and Pierre Joseph Henry Baudet.- 38. Monochromatic Arithmetic Progressions or Life After Van der Waerden.- 39. In Search of Van der Waerden: The Early Years.- 40. In Search of Van der Waerden: The Nazi Leipzig, 1933–1945.- 41. In Search of Van der Waerden: Amsterdam, Year 1945.- 42. In Search of Van der Waerden: The Unsettling Years, 1946–1951.- 43. How the Monochromatic AP Theorem Became Classic: Khinchin and Lukomskaya.- VIII. Colored Polygons: Euclidean Ramsey Theory.- 44. Monochromatic Polygons in a 2-Colored Plane.- 45. 3-Colored Plane, 2-Colored Space, and Ramsey Sets.- 46. The Gallai Theorem.- IX. Colored Integers in Service of the Chromatic Number of the Plane: How O’Donnell Unified Ramsey Theory and No One Noticed.- 47. O'Donnell Earns His Doctorate.- 48. Application of Baudet–Schur–Van der Waerden.- 48. Application of Bergelson–Leibman’s and Mordell–Faltings’ Theorems.- 50. Solution of an Erdős Problem: The O’Donnell Theorem.- X. Ask What Your Computer Can Do for You.- 51. Aubrey D.N.J. de Grey's Breakthrough.- 52. De Grey's Construction.- 53. Marienus Johannes Hendrikus 'Marijn' Heule.- 54. Can We Reach Chromatic 5 Without Mosers Spindles?.- 55. Triangle-Free 5-Chromatic Unit Distance Graphs.- 56. Jaan Parts' Current World Record.- XI. What About Chromatic 6?.- 57. A Stroke of Brilliance: Matthew Huddleston's Proof.- 58. Geoffrey Exoo and Dan Ismailescu or 2 Men from 2 Forbidden Distances.- 59. Jaan Parts on Two-Distance 6-Coloring.- 60. Forbidden Odds, Binaries, and Factorials.- 61. 7-and 8-Chromatic Two-Distance Graphs.- XII. Predicting the Future.- 62. What If We Had No Choice?.- 63. AfterMath and the Shelah–Soifer Class of Graphs.- 64. A Glimpse into the Future: Chromatic Number of the Plane, Theorems and Conjectures.- XIII. Imagining the Real, Realizing the Imaginary.- 65. What Do the Founding Set Theorists Think About the Foundations?.- 66. So, What Does It All Mean?.- 67. Imagining the Real or Realizing the Imaginary: Platonism versus Imaginism.- XIV. Farewell to the Reader.- 68. Two Celebrated Problems.- Bibliography.- Name Index.- Subject Index.- Index of Notations.