Endre Szemerédi (born August 21, 1940) is a Hungarian–American mathematician celebrated for deep results in combinatorics, number theory and theoretical computer science. He is best known for the result now called Szemerédi's theorem, a landmark statement about arithmetic progressions in large sets of integers. Szemerédi has held the State of New Jersey Professorship of Computer Science at Rutgers University since 1986 and is a professor emeritus at the Alfréd Rényi Institute of Mathematics.
Major contributions
Szemerédi's work spans several interlocking areas of discrete mathematics. His most famous theorem asserts that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions; this result united combinatorics and number theory and has inspired alternative proofs and extensions from ergodic theory and harmonic analysis. He also introduced a fundamental tool in extremal graph theory, the Szemerédi regularity lemma, which provides a structural decomposition of large graphs and underpins many advances in graph algorithms and property testing.
Selected results and influence
- Szemerédi's theorem on arithmetic progressions, a cornerstone of additive combinatorics.
- The Szemerédi regularity lemma, used widely in graph theory and theoretical computer science.
- Collaborative results and problems that stimulated later breakthroughs, including applications in the theory of prime numbers and algorithmic combinatorics.
Connections to other approaches are notable: H. Furstenberg provided an ergodic-theoretic proof that opened new perspectives, and later work by Green and Tao on arithmetic progressions in the primes built on ideas from Szemerédi's theorem. His methods and concepts appear frequently in algorithmic contexts, complexity theory and discrete geometry.
Career and legacy
Born in Budapest, Szemerédi has maintained strong ties to the Hungarian mathematical community while working in the United States. His scholarship has influenced generations of researchers and produced tools that are standard in modern combinatorics and theoretical computer science. For further details on his publications and biography, see biographical resources and lists of selected papers. Additional overviews of his methods appear in surveys on additive combinatorics and graph regularity.
Academic profiles and institutional pages provide up-to-date information about positions, talks and honors; consult his faculty page at Rutgers (Rutgers profile) and the Rényi Institute (Rényi Institute page) for authoritative listings. Szemerédi's theorems and tools remain central to current research and teaching in discrete mathematics and theoretical computer science.