* 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.