# 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 earned his degree in 1967 (doctoral exam ) and in 1969 received his doctorate in Jan Popken ( 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 1970/71 at the Institute for Advanced Study. In 1971 he became assistant professor in 1975 and professor at Leiden University, where he was from 1991 to 1993 Chairman of the Department of Mathematics and computer science. He has been a visiting professor at Cambridge University (1976 ), the University of Michigan (1976 ), ETH Zurich (1980 ), the University of Pisa (1983 ), at the Tata Institute of Fundamental Research (1991, 2000), the University of Paris VII ( University of Paris -Diderot ), Canada, Japan, Sydney ( University of New South Wales) and the Mathematical Sciences Research Institute ( MSRI ) in Berkeley. Since 1999 he is Director of the Thomas Stieltjes Institute for Mathematics.

## Work

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

The Catalan problem is a special case of exponential Diophantine equations with which Tijdeman addressed. In 1976 he proved using methods from the theory of transcendental numbers the set of Tijdeman ( Acta Arithmetica vol 29, 1976, p 197), which states that

For m, n> 1 only finitely many integer solutions x, y has. The number of consecutive powers of integers is finite. The 2002 proved by Preda Mihăilescu Catalan 's conjecture states that the equation has only one solution (x = 3, y = 2, m = 2, n = 3).

## Memberships and Miscellaneous

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

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 appointed Knight of the Order of the Netherlands Lion.

He is married and has two children.

## Writings

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