On the Mathematical Basis of Computer Science

Summary

It is now clear to anybody that a working mathematician cannot ignore computers: as a consequence, it is commonly admitted that students in mathematics, and especially those who intend to become teachers in the field, have to be exposed to some high-level language (such as PASCAL). Nevertheless, this is far from being enough: the question whether students in mathematics should be familiar with some parts of the theoretical foundations of computer science cannot be avoided because these topics are precisely the parts of computer science close to mathematics and seem to be necessary in order to establish between both fields connections that go beyond the ability of using the computing power of modern machines.

In France, following these line of ideas, an optional test in computer science is now offered in the well-established “Concours d'Agrégation de mathématiques”. It is not my purpose to discuss the role of the Agrégation in the French academic system: for those who are not familiar with this system, let me simply say that the Agrégation is a quite selective competitive exam which can be defined as a “teaching Ph.D.” and that many of the teachers for the age-group 17-22 have passed this exam. This is enough to understand why the fact that was quoted above might be more important than appears at first glance: it is likely that most of the requirements for the computer science test of the Agrégation will become part of the standard curriculum leading to graduation in mathematics.