József Beck (

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

Hungary Hungary ( hu, Magyarország ) is a landlocked country in Central Europe. Spanning of the Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the south, Croatia a ...

, February 14, 1952) is a Harold H. Martin Professor of

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...

. His contributions to

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

include the

partial colouring lemma Partial may refer to: Mathematics *Partial derivative, derivative with respect to one of several variables of a function, with the other variables held constant ** ∂, a symbol that can denote a partial derivative, sometimes pronounced "partial d ...

and the

Beck–Fiala theorem In mathematics, the Beck–Fiala theorem is a major theorem in discrepancy theory due to József Beck József Beck (Budapest, Hungary, February 14, 1952) is a Harold H. Martin Professor of Mathematics at Rutgers University. His contributions to ...

in ''

discrepancy theory In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be in. It is also called the theory of irregularities of distribution. This refers to the theme of ''classical'' discrepancy theory, name ...

'', the algorithmic version of the

Lovász local lemma In probability theory, if a large number of events are all independent of one another and each has probability less than 1, then there is a positive (possibly small) probability that none of the events will occur. The Lovász local lemma allows one ...

, the two extremes theorem in combinatorial geometry and the

second moment method In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive. More generally, the "moment method" consists of bounding the probability th ...

in the theory of positional games, among others. Beck was awarded the Fulkerson Prize in 1985 for a paper titled ''"Roth's estimate of the discrepancy of integer sequences is nearly sharp"'', which introduced the notion of discrepancy on hypergraphs and established an upper bound on the discrepancy of the family of arithmetic progressions contained in , matching the classical lower bound up to a

polylogarithm In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function of order and argument . Only for special values of does the polylogarithm reduce to an elementary function such as the natur ...

ic factor. Jiří Matoušek and Joel Spencer later succeeded in getting rid of this factor, showing that the bound was really sharp. Beck gave an invited talk at the 1986

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

. He is an external member of the

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its ma ...

(2004).

Books

*''Irregularities of Distribution'' (with William W. L. Chen, Cambridge Tracts in Mathematics 89, Cambridge University Press, 1987) *'' Combinatorial Games: Tic-Tac-Toe Theory'' (Encyclopedia of Mathematics and its Applications 114, Cambridge University Press, 2008) *''Inevitable Randomness in Discrete Mathematics (University Lecture Series 49, American Mathematical Society, 2009)'' *''Probabilistic Diophantine Approximation: Randomness in Lattice Point Counting'' (Springer Monographs in Mathematics. Springer-Verlag, 2014) *''Strong Uniformity and Large Dynamical Systems'' (World Scientific Publishing, 2018)

References

External links

József Beck, personal webpage
Department of Mathematics,

József Beck
Mathematics Genealogy Project Mathematicians from Budapest Members of the Hungarian Academy of Sciences 1952 births Living people Rutgers University faculty Positional games Hungarian emigrants to the United States {{Europe-mathematician-stub