Ramsey Theory : Yesterday Today and Tomorrow Ramsey theory is a relatively “new ” approximately 100 year old direction of fascinating mathematical thought that touches on many classic fields of mathematics such as combinatorics number theory geometry ergodic theory topology combinatorial geometry set theory and measure theory. Ramsey theory possesses its own unifying ideas and some of its results are among the most beautiful theorems of mathematics. The underlying theme of Ramsey theory can be formulated as: any finite coloring of a large enough system contains a monochromatic subsystem of higher degree of organization than the system itself or as T.S. Motzkin famously put it absolute disorder is impossible. Ramsey Theory: Yesterday Today and Tomorrow explores the theory’s history recent developments and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike. Contributors: J. Burkert A. Dudek R.L. Graham A. Gyárfás P.D. Johnson Jr. S.P. Radziszowski V. Rödl J.H. Spencer A. Soifer E. Tressler. How This Book Came into Being Table of Contents Ramsey Theory before Ramsey Prehistory and Early History: An Essay in 13 Parts Eighty Years of Ramsey R(3 k). . . and Counting! Ramsey Numbers Involving Cycles On the function of Erdὅs and Rogers Large Monochromatic Components in Edge Colorings of Graphs Szlam’s Lemma: Mutant Offspring of a Euclidean Ramsey Problem: From 1973 with Numerous Applications Open Problems in Euclidean Ramsey Theory Chromatic Number of the Plane and Its Relatives History Problems and Results: An Essay in 11 Parts Euclidean Distance Graphs on the Rational Points Open Problems Session.