Where do mutations come from, and what do they have to do with mathematics? A lot, as this article will demonstrate. Indeed, it was a historical milestone of mathematical biology that revealed some fundamental insight into the nature of mutations during the 1940’s. An unresolved question in those days was: ‘Are mutations due to directed adaptation to environmental change, or do they occur
... [Show full abstract] spontaneously, in a random way?’ Today, the answer is basic knowledge in genetics, and many textbooks briefly describe the crucial experiment, along with some plausibility arguments. It is hardly known, however, that it was a fascinating interaction of theory and experiment that made this breakthrough possible.