Erdös Centennial

1. Front Matter

   Pages 1-10

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2. Paul Erdős and Probabilistic Reasoning

   • Noga Alon

   Pages 11-33

3. Euclidean vs. Graph Metric

   • Itai Benjamini

   Pages 35-57

4. The Phase Transition in the Erdős-Rényi Random Graph Process

   • Béla Bollobás, Oliver Riordan

   Pages 59-110

5. Around the Sum-product Phenomenon

   • Jean Bourgain

   Pages 111-128

6. Small Doubling in Groups

   • Emmanuel Breuillard, Ben Green, Terence Tao

   Pages 129-151

7. Erdős and Multiplicative Number Theory

   • Harold G. Diamond

   Pages 153-168

8. The History of Degenerate (Bipartite) Extremal Graph Problems

   • Zoltán Füredi, Miklós Simonovits

   Pages 169-264

9. Erdős and Arithmetic Progressions

   • W. Timothy Gowers

   Pages 265-287

10. Paul Erdős and Egyptian Fractions

    • Ronald L. Graham

    Pages 289-309

11. Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions, II

    • Kálmán Győry

    Pages 311-324

12. Erdős’s Work on Infinite Graphs

    • Péter Komjáth

    Pages 325-345

13. The Impact of Paul Erdős on Set Theory

    • Kenneth Kunen

    Pages 347-363

14. Some Problems and Ideas of Erdős in Analysis and Geometry

    • R. Daniel Mauldin

    Pages 365-376

15. L ² Majorant Principles

    • Hugh L. Montgomery

    Pages 377-381

16. A Combinatorial Classic — Sparse Graphs with High Chromatic Number

    • Jaroslav Nešetřil

    Pages 383-407

17. Small Ball Probability, Inverse Theorems, and Applications

    • Hoi H. Nguyen, Van H. Vu

    Pages 409-463

18. The Beginnings of Geometric Graph Theory

    • János Pach

    Pages 465-484

19. Paul Erdős and the Difference of Primes

    • János Pintz

    Pages 485-513

20. Paul Erdős and the Rise of Statistical Thinking in Elementary Number Theory

    • Paul Pollack, Carl Pomerance

    Pages 515-533

Paul Erdös was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments. 

• combinatorics
• number theory
• probabilistic method
• set theory

From the book reviews:

“Paul Erdős was a very influential mathematician. … The volume is an invaluable source for those students and researchers who are touched by Erdős’ mathematics.” (Péter Hajnal, Acta Scientiarum Mathematicarum (Szeged), Vol. 80 (1-2), 2014)

• Department of Computer Science, Eötvös Lóránd University, Budapest, Hungary

  László Lovász

• Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

  Imre Z. Ruzsa, Vera T. Sós

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