IX. Conclusion

The title of my talk (impact of chaos on mathematics) suggests a one-way relation, with mathematics at the receiving end. A card carrying mathematician could well argue in the opposite direction, and quote the party slogan about mathematics being the "queen and servant" of other sciences. What I have tried to show is that, in the case at hand, the relations of mathematics with physics (or more generally the natural sciences) have been more subtle and interesting than one might a priori imagine. Physics has provided some questions and some answers to mathematics. Mathematics has provided its own way of thinking about problems, which is more important than ready-made answers and theorems. Physicists have been functioning as mathematicians and vice-versa, and the result has been a decade or two of exceptionally fruitful intellectual work, with benefit both to mathematics, and to the physics of chaos.