Endre Szemerédi (Hungarian: [ˈɛndrɛ ˈsɛmɛreːdi]; born August 21, 1940) is a Hungarian-American mathematician, working in the field of combinatorics and theoretical computer science. He has been the State of New Jersey Professor of computer science at Rutgers University since 1986. He also holds a professor emeritus status at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences.
Szemerédi has won prizes in mathematics and science, including the Abel Prize in 2012. He has made a number of discoveries in combinatorics and computer science, including Szemerédi's theorem, the Szemerédi regularity lemma, the Erdős–Szemerédi theorem, the Hajnal–Szemerédi theorem and the Szemerédi–Trotter theorem.
Szemerédi was born in Budapest. Since his parents wished him to become a doctor, Szemerédi enrolled at a college of medicine, but he dropped out after six months (in an interview he explained it: "I was not sure I could do work bearing such responsibility."). He studied in Eötvös Loránd University in Budapest and received his PhD from Moscow State University. His adviser was Israel Gelfand. This stemmed from a misspelling, as Szemerédi originally wanted to study with Alexander Gelfond.
Szemerédi has been the State of New Jersey Professor of computer science at Rutgers University since 1986. He has held visiting positions at Stanford University (1974),McGill University (1980), the University of South Carolina (1981–1983) and the University of Chicago (1985–1986).
Endre Szemerédi has published over 200 scientific articles in the fields of discrete mathematics, theoretical computer science, arithmetic combinatorics and discrete geometry. He is best known for his proof from 1975 of an old conjecture of Paul Erdős and Pál Turán: if a sequence of natural numbers has positive upper density then it contains arbitrarily long arithmetic progressions. This is now known as Szemerédi's theorem. One of the lemmas introduced in his proof is now known as the Szemerédi regularity lemma, which has become an important lemma in combinatorics, being used for instance in property testing for graphs and in the theory of graph limits.
He is also known for the Szemerédi–Trotter theorem in incidence geometry and the Hajnal–Szemerédi theorem in graph theory. Ajtai and Szemerédi proved the corners theorem, an important step toward higher-dimensional generalizations of the Szemerédi theorem. With Ajtai and Komlós he proved the ct2/log t upper bound for theRamsey number R(3,t), and constructed a sorting network of optimal depth. With Ajtai, Chvátal, and M. M. Newborn, Szemerédi proved the famous Crossing Lemma, that a graph with n vertices and m edges, wherem > 4n has at least m3 / 64n2 crossings. With Paul Erdős, he proved the Erdős–Szemerédi theorem on the number of sums and products in a finite set. With Wolfgang Paul, Nick Pippenger, and William Trotter, he established a separation between nondeterministic linear time and deterministic linear time, in the spirit of the infamous P versus NP problem.
Szemerédi has won numerous awards and honors for his contribution to mathematics and computer science. A few of them are listed here:
Szemerédi is a corresponding member (1982), and member (1987) of the Hungarian Academy of Sciences and a member (2010) of the National Academy of Sciences. He is also a member of the Institute for Advanced Study (IAS), Princeton, NJ and a permanent research fellow at the Rényi Institute of Mathematics, Budapest.
He was the Fairchild Distinguished Scholar at CALTECH in 1987–88.
He was the lecturer in the Forty-Seventh Annual DeLong Lecture Series at University of Colorado.
In 2012, Szemerédi was awarded the Abel Prize “for his fundamental contributions to discrete mathematics and theoretical computer science, and in recognition of the profound and lasting impact of these contributions on additive number theory and ergodic theory” The Abel Prize citation also credited Szemerédi with bringing combinatorics to the centre-stage of mathematics and noted his place in the tradition of Hungarian mathematicians such as George Pólya who emphasized a problem-solving approach to mathematics. Szemerédi reacted to the announcement by saying that "It is not my own personal achievement, but recognition for this field of mathematics and Hungarian mathematicians," that gave him the most pleasure.