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Updated: March 22, 2012 03:34 IST

Hungarian mathematician Endre Szemerédi gets 2012 Abel Prize

R. Ramachandran
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Endre Szemeredi. Photo: By Special Arrangement
Endre Szemeredi. Photo: By Special Arrangement

The winner of the prestigious Abel Prize of the Norwegian Academy of Science and Letters for the year 2012 is 72-year-old Hungarian mathematician Endre Szemerédi of the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, and Department of Computer Science, Rutgers, The State University of New Jersey in the United States.

Szemerédi's highly influential work has proved to be a game-changer in many areas of mathematics.

The announcement was made by the President of the Norwegian Academy in Oslo on Tuesday and the award is being given “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.”

Szemerédi has been described as a mathematician with exceptional research power and his influence in diverse areas of present-day mathematics has been enormous. The festschrift volume, titled An Irregular Mind, published on his 70th birthday, ascribes his unique way of thinking and extraordinary mathematical vision as perhaps due to his brain being wired differently — “an irregular mind” — than most mathematicians.

Discrete mathematics is the study of structures such as graphs, sequences, permutations and geometric configurations and it is the mathematics of such structures that forms the foundation of theoretical computer science and information theory. For example, the tools of graph theory can be used to analyse communication networks such as the Internet. Similarly, the designing of efficient computational algorithms relies crucially on insights from discrete mathematics.

Szemerédi, says the citation, “has revolutionized discrete mathematics by introducing ingenious and novel techniques, and by solving many fundamental problems”. His work has brought combinatorics to the centre-stage of mathematics by bringing to bear its application in many areas of mathematics such as additive number theory, ‘ergodic' theory, theoretical computer science and ‘incidence' geometry.

The Abel Committee has noted that Szemerédi's approach belongs to the strong Hungarian problem-solving tradition exemplified by mathematicians such as George Pólya and yet the theoretical impact of his work has been enormous.

Interestingly, Szemerédi entered mathematics somewhat late. He attended medical school for a year and worked in a factory before switching to mathematics. His extraordinary mathematical talent was discovered when he was a young student in Budapest by his mentor, famous Hungarian mathematician Paul Erdõs. He studied at the Eõtvõs Loránd University in Budapest and obtained his Ph.D. in 1970 under Israel M. Gelfand at Moscow State University.

Szemerédi proved several fundamental theorems of tremendous importance. Many of his results have opened up new avenues in mathematics and form the basis for future research. He first attracted international attention in 1976 with his solution of what is known as the Erdõs-Turan Conjecture. In its proof, Szemerédi had used a masterpiece of combinatorial reasoning, which was immediately recognised to have exceptional depth and power. A key step in the proof, now known as the Szemerédi Regularity Lemma, is used for classification of large graphs.

Many of Szemerédi's discoveries that have had great impact on discrete mathematics and theoretical computer science carry his name. Examples in discrete mathematics include the Szemerédi-Trotter Theorem, the Ajtai-Komlós-Szemerédi semi-random method, the Erdõs-Szemerédi sum-product theorem, and the Balog-Szemerédi-Gowers Lemma. Examples in theoretical computer science include the Ajtai-Komlós-Szemerédi sorting network, the Fredman-Komlós-Szemerédi hashing scheme and the Paul-Pippenger-Szemerédi-Trotter theorem.

The Abel Prize, named after great Norwegian mathematical genius Niels Henrik Abel (1802-1829), is given in recognition of outstanding contributions to mathematical sciences and has been awarded annually since 2003.

Abel, who died at the age of 26, has often been compared with the Indian mathematical genius Srinivasa Ramanujan. The Prize was established in 2001 as part of Abel's 200th birth anniversary. It carries a cash award of 6 million Norwegian Kroner (NOK), equivalent to €750,000 (about U.S$ 1 million), and is comparable in prestige, value and eligibility criterion to the Nobel Prize, which, does not cover mathematics.

The winning candidate is selected on the basis of the recommendation of an international committee of outstanding mathematicians chaired by a Norwegian. The current committee is headed by Ragni Piene, Professor at the University of Oslo and includes M.S. Raghunathan, formerly of the Tata Institute of Fundamental research (TIFR) and currently at the Indian Institute of Technology-Bombay (IIT-B), in Mumbai.

The selection of Szemerédi for the award was made in February at a meeting of the Committee held at the TIFR.

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