Cognitive Mobility, a Macroscopic Investigation of Migration of Scientists between Research Fields Studied by Example of Mathematics. — In history of science, scientific migrations of famous scientists are well-known. Nothing is known, however, about the total of migrations between fields of science, despite the importance of scientific mobility for information transfer and exchange. In the present investigation all migrations between the major 39 subdisciplines of mathematics from 1959 through 1975 are studied in a macroscopic manner. The quantitative importance of migration (...) for the development of mathematical fields is assessed. In an analysis of the relationship between the affinity of fields and mobility between them a „principle of least migration distance” is established. Furthermore, some aspects of a Markov-chain treatment of scientific mobility are discussed. (shrink)