This is not a review, but an introductory discussion, including a few selected references, of the meaning and significance of the currently evolving concept of a mathematical medicine. It will be seen that mathematical medicine is crystallizing out of a wide spectrum of mathematically oriented biological, medical and biomedical subdisciplines. This discussion stresses the relationships of the points of view and methodologies in these areas to those of the Science and Art of Medicine and to medical education as demonstrated by a few examples from the literature.