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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.

Graph coloring. --- Graph theory. --- Mathematics. --- Ramsey numbers. --- Ramsey theory -- History. --- Ramsey theory. --- Ramsey theory --- Ramsey numbers --- Graph theory --- Graph coloring --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- History --- Dynamics. --- Ergodic theory. --- Convex geometry. --- Discrete geometry. --- Combinatorics. --- Dynamical Systems and Ergodic Theory. --- Convex and Discrete Geometry. --- Combinatorial analysis --- Differentiable dynamical systems. --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Combinatorics --- Mathematical analysis --- Discrete mathematics --- Convex geometry . --- Geometry --- Combinatorial geometry --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics