Endre Szemerédi Receives 2008 Steele Prize for a Seminal Contribution to Research Achievement

January 7, 2008

Providence, RI:

Endre Szemerédi of Rutgers University and the Alfred Renyi Institute in Budapest has received the 2008 AMS Leroy P. Steele Prize for a Seminal Contribution to Research. Presented annually by the American Mathematical Society, the Steele Prize is one of the highest distinctions in mathematics. The prize was awarded today at the Joint Mathematics Meetings in San Diego, California.

Endre Szemerédi is honored for his paper "On sets of integers containing no k elements in arithmetic progression", Acta Arithmetica XXVII (1975), pages 199-245. This landmark paper solved an outstanding problem first posed in 1936 by Paul Erdös and Pál Turán. The problem concerns arithmetic progressions, which are sequences of whole numbers that differ by a fixed amount. For example, 3, 5, 7 is an arithmetic progression of length 3, where the numbers differ by 2; 109, 219, 329, 439, 549 is a progression of length 5, where the numbers differ by 110. Erdös and Turán conjectured that sets of integers that obey a certain condition (called "positive density") would contain infinitely long arithmetic progressions. Endre Szemerédi proved this conjecture in his paper.

"The solution is a true masterpiece of combinatorics, containing new ideas and tools whose impact go well beyond helping to solve a specific hard problem," the citation says of Endre Szemerédi's paper. "One of these new tools, his by now famous Regularity Lemma, has become a foundation of modern combinatorics... Beyond combinatorics, [the lemma] has found applications in number theory and in computer science, in particular in complexity theory."
 

Endre Szemerédi's paper stimulated other mathematicians to find new proofs of the Erdös-Turán conjecture, and these brought new ideas and understanding. Also following in the footsteps of Endre Szemerédi was work a few years ago by Ben Green and Terence Tao, which drew huge attention among mathematicians by showing that there exist arbitrarily long arithmetic progressions of prime numbers.

Find out more about AMS prizes at http://www.ams.org/prizes-awards.

Contact :
Public Awareness Office
American Mathematical Society
201 Charles St.
Providence, RI 02904
Email: paoffice at ams dot org
Phone: 401-455-4000
Fax: 401-331-3842

Founded in 1888 to further mathematical research and scholarship, the 30,000-member American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.