Reflections on Paul Erdős on His Birth Centenary, Part II

Krishnaswami Alladi, Steven Krantz, Noga Alon, D. A. Goldston, András Sárközy, József Szabados, Gérald Tenenbaum, Stephan Ramon Garcia, Amy L. Shoemaker
2015 Notices of the American Mathematical Society  
Paul Erdős and the Probabilistic Method Probabilistic Beginnings The probabilistic method is one of the most significant contributions of Paul Erdős. Indeed, Paul himself said, during his eightieth birthday conference in Keszthely, Hungary, that he believes the method will live long after him. This was the only time I heard him making any comment about the significance and impact of his work. He was always more interested in discussing new problems and results than in trying to assess their
more » ... -time expected merits. The method is a powerful technique with numerous applications in combinatorics, graph theory, additive number theory and geometry. Theorem 1 ([25], [1]). There are two absolute positive constants c 1 , c 2 such that c 1 m 2 / log m ≤ r (K 3 , K m ) ≤ c 2 m 2 / log m for all m > 1. March 2015
doi:10.1090/noti1223 fatcat:oo4u652qrrfizkj22kko6kmwqa