*Programme leaders: H.W. Lenstra, R. Tijdeman*

Number theory studies the properties of integers, with a historically strong emphasis on the study of diophantine equations, that is, systems of equations that are to be solved in integers. The methods of number theory are taken from several other branches of mathematics.

Traditionally, these include algebra and analysis, but in recent times algebraic geometry has been playing a role of increasing importance as well. It has also been discovered that number theory has important applications in more applied areas, such as cryptography, theoretical computer science, dynamical systems theory and numerical mathematics. These new developments stimulated the design, analysis and use of algorithms, now called computational number theory. They led to a unification rather than diversification of number theory.

For example, the applications in cryptography are strongly connected to algebraic geometry and computational number theory; and algebraic number theory, which used to stand on itself, is now pervading virtually all of number theory.

Themes of the program reflect the mentioned research areas. They include finding points on algebraic curves, applications of group theory and algebraic number theory, the theory of finite fields, diophantine approximation, words and sequences, discrete tomography, primality tests and factorization methods, and the development of efficient computer algorithms.

The biweekly national Intercity Number Theory Seminar continued to be the meeting place for the participants. Besides there were several activities supported by the Spinoza grant of H.W. Lenstra, the Stieltjes Institute, the Lorentz Center and NWO.

The instructional Stieltjes week on Explicit Algebraic Number Theory was well attended and appreciated. So was the subsequent NWO-OTKA workshop with the same title.

The project to fill the white spot in Escher's lithograph "Prentententoonstelling" was particularly successful. In numerous publications and lectures Lenstra, De Smit and others explained the application of mathematical research to art showing how mathematical analysis helps in explaining structure.