Mathematicianâs âIrregular Mindâ Scoops Abel Award
An âirregular mindâ is what has won this yearâs Abel Prize, one of the most prestigious awards in mathematics, for Endre SzemerĂ©di of the AlfrĂ©d RĂ©nyi Institute of Mathematics in Budapest.
That is how SzemerĂ©di (pronounced sem-er-ADY) was described in a book published two years ago to mark his 70th birthday, which added that âhis brain is wired differently than for most mathematiciansâ.
SzemerĂ©di was awarded the prize, worth 6 million Norwegian kroner (about US$1 million), âfor 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 theoryâ, according to the Norwegian Academy of Science and Letters, which awarded the first Abel prize as a kind of mathematics Nobel in 2003.
Discrete mathematics deals with mathematical structures that are made up of discrete entities rather than smoothly varying ones: for example, integers and point networks. Crudely speaking, it involves a kind of digital rather than analogue maths, which helps to explain its relationship to aspects of computer theory, particularly logic operations.
Nils Stenseth, president of the academy, who announced the award today, says that SzemerĂ©diâs work shows how research that is purely curiosity-driven can turn out to have important practical applications. âSzemerĂ©diâs work supplies some of the basis for the whole development of informatics and the Internetâ, he says. âHe showed how number theory can be used to organize large amounts of information in efficient ways.â
Szemerédi began his training not in maths, but at medical school. He was spotted and mentored by another Hungarian pioneer, Paul Erdös, widely regarded as one of the greatest mathematicians of the twentieth century.
One of his first successes was a proof of a conjecture made in 1936 by Erdös and his colleague Paul TurĂĄn concerning the properties of integers. They aimed to establish criteria for whether a series of integers contains arithmetic progressions: that is, sequences of integers that differ by the same amount, such as 3, 6, 9âŠ
In 1975 SzeremĂ©di showed that subsets of any large enough string of integers must contain arithmetic progressions of almost any length. In other words, if you had to pick, say, 1% of all the numbers between 1 and some very large number N, you canât avoid selecting some arithmetic progressions. This was the Erdös-TĂșran conjecture, now supplanted by SzemerĂ©diâs theorem.
The result connected work on number theory to graph theory, the mathematics of networks of connected points. The connection is most famously revealed by the four-colour theorem, which states that it is possible to colour any map (considered as a network of boundaries) with four colours such that no two regions with the same colour share a border. The mathematics involved is somewhat analogous to finding arithmetic progressions in strings of âcolouredâ integers.
Deep connections