Abstract

SummaryA discussion of the relations between mathematics and reality has a double aspect: it may concern the status of mathematical concepts and their right to be considered as part of “reality”. But the history of scientific concepts shows that attempts to single out a so‐called reality are arbitrary and futile, and the intrusion of ontological thinking in science apparently has never been fruitful.Another way to look at the problem is to investigate the use of mathematical methods to attain knowledge or power about “reality”, by which is generally meant physics . Many examples from the history of sciences show that it is almost impossible to tell in advance whether a mathematical concept or theory will be useful or not.For the time being, it has not yet been possible to apply mathematics in a significant and pregnant way to various sciences. It is advocated that what is needed are not sophisticated mathematical developments, but some rather simple mathematical structures that still have to be described and applied. The present trends in mathematics, which emphasize the understanding of simple and basic mathematical concepts, allow us to hope that significant progress in these directions can be expected