Mathematics Department - News Item: Endre Szemerédi Receives 2008 Steele Prize and 2008 Rolf Schock Prize

# News Item: Endre Szemerédi Receives 2008 Steele Prize and 2008 Rolf Schock Prize

Professor Endre Szemerédi, New Jersey Professor of Computer Science and Associate Member of the Department of Mathematics, received the Leroy P. Steele Prize for Seminal Contribution to Research of the American Mathematical Society in January, 2008. In May, 2008 he was named the recipient of the 2008 Rolf Schock Prize in Mathematics of the Swedish Royal Academy of Sciences.

The Steele Prize honored Professor Szemerédi's paper "On sets of integers containing no k elements in arithmetic progression," Acta Arithmetica XVII (1975), 199-245, in which he established a 39-year-old conjecture of Paul Erdős and Paul Turán: Every set of integers of positive density contains arithmetic progressions of arbitrary length. The citation states:

"[Szemerédi's proof] is a true masterpiece of combinatorics, containing new ideas and tools whose impact go well beyond helping to solve a specific hard problem. One of these tools, his by now famous Regularity Lemma, has become a foundation of modern combinatorics...It is fair to say that the Regularity Lemma has transformed graph theory fromm the study of special graphs and of extremal problems to the study of general graphs and random graphs. Beyond combinatorics it has found application in number theory and in computer science, in particular in complexity theory.

"However, the impact of Szemerédi's paper goes beyond this. The solution of the Erdős-Turán conjecture stimulated other mathematicians [Furstenberg, Gowers] to find new methods of attack...More recently, Green and Tao were able to replace the positive density condition in Szemerédi's theorem by other arithmetical conditions, which allowed them ... to prove the same result for any sequence of primes of relative positive density, thereby solving another famous conjecture of Erdős considered inaccessible by standard methods of analytic number theory."

The citation for the Rolf Schock Prize was "for his deep and pioneering work from 1975 on arithmetic progressions in subsets of the integers, which has led to great progress and discoveries in several branches of mathematics."

The Steele Prize is presented annually at the national meeting of the American Mathematical Society, and carries a $5,000 award. The Rolf Schock Prizes are awarded every three years; the first awards were made in 1993. Four prizes are given, in Philosophy, Mathematics, Fine Arts, and Music, by the various Swedish Royal Academies. The four 2008 awardees will share a prize of SEK 2,000,000 (about US$333,000).

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