József Beck (

Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...

Hungary Hungary is a landlocked country in Central Europe. Spanning much of the Pannonian Basin, 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 and ...

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

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

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

. His contributions to

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

include the partial colouring lemma and the

Beck–Fiala theorem In mathematics, the Beck–Fiala theorem is a major theorem 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 ...

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, nam ...

'', 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 a s ...

, the two extremes theorem in

combinatorial geometry Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geom ...

and the second moment method in the theory of

positional game A positional game in game theory is a kind of a combinatorial game for two players. It is described by: *Xa finite set of elements. Often ''X'' is called the ''board'' and its elements are called ''positions''. *\mathcala family of subsets of ...

s, among others. Beck was awarded the

Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e ...

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

hypergraph In mathematics, a hypergraph is a generalization of a Graph (discrete mathematics), graph in which an graph theory, edge can join any number of vertex (graph theory), vertices. In contrast, in an ordinary graph, an edge connects exactly two vert ...

s and established an upper bound on the discrepancy of the family of

arithmetic progression An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that ...

s 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 Joel Spencer (born April 20, 1946) is an American mathematician. He is a combinatorialist who has worked on probabilistic methods in combinatorics and on Ramsey theory. He received his doctorate from Harvard University in 1970, under the supervis ...

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 IMU Abacus Medal (known before ...

. He is an external member of the

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( , MTA) is Hungary’s foremost and most prestigious learned society. Its headquarters are located along the banks of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. The Academy's primar ...

(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 The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. it contained information on 300,152 mathematical scientists who contributed to research-level mathematics. For a typical mathematicia ...

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