Robert Tijdeman

Robert Tijdeman (born July 30, 1943 in Oostzaan ) is a Dutch mathematician who deals with number theory and combinatorics.

Career

Tijdeman studied from 1961 at the University of Amsterdam , where he graduated in 1967 (doctoral examination) and received his doctorate in 1969 under Jan Popken ( on the distribution of the value of certain functions ). From 1967 he was a scientist at the University of Amsterdam. In 1968/69 he was at the Academy of Sciences in Budapest and in 1970/71 at the Institute for Advanced Study . In 1971 he became assistant professor and in 1975 professor at the University of Leiden , where he was chairman of the faculty for mathematics and computer science from 1991 to 1993. He was visiting professor at Cambridge University (1976), the University of Michigan (1976), the ETH Zurich (1980), the University of Pisa (1983), the Tata Institute of Fundamental Research (1991, 2000), the University of Paris VII (University of Paris-Diderot), in Canada, Japan, Sydney ( University of New South Wales ) and at the Mathematical Sciences Research Institute (MSRI) in Berkeley. Since 1999 he has been director of the Thomas Stieltjes Institute for Mathematics.

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Tijdeman is an internationally known number theorist who dealt, among other things, with the theory of transcendent numbers , the Catalan problem and the abc conjecture . He has also published with Paul Erdős and Andrzej Schinzel , TN Shorey , Cameron L. Stewart and Alf van der Poorten . Tijdeman also dealt with algorithms for computed tomography .

The Catalan problem is a special case of exponential Diophantine equations that Tijdeman dealt with. In 1976 he used methods from the theory of transcendent numbers to prove Tijdeman's theorem ( Acta Arithmetica Vol. 29, 1976, p. 197), which says that

${\displaystyle x^{m}=y^{n}+1}$

for m, n> 1 only has finitely many integer solutions x, y. The number of consecutive powers of whole numbers is finite. The Catalan conjecture, proven by Preda Mihăilescu in 2002, states that the equation has only one solution (x = 3, y = 2, m = 2, n = 3).

Memberships and miscellaneous

Since 1987 he has been a member of the Dutch Academy of Sciences . He is a member of the Dutch, German (since 1990), French, American mathematical societies and the London Mathematical Society . From 1982 to 1984 he was Vice President and 1984 to 1986 President of the Dutch Mathematical Society. He is an honorary doctor from the University of Debrecen . He has been co-editor of Acta Arithmetica since 1981, editor of Indagationes Mathematicae from 1988 to 1993 and editor of Compositio Mathematica from 1980 to 1992.

In 1978 he was invited speaker at the International Congress of Mathematicians (ICM) in Helsinki ( On exponential diophantine equations ).

On the occasion of his retirement in 2008 he was made a Knight of the Order of the Dutch Lion .

He is married and has two children.

Fonts

• TN Shorey, Tijdeman Exponential diophantine equations , Cambridge University Press, Cambridge Tracts in Mathematics, 1986

Web links

• Homepage in Leiden