When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians," many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity;, f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery." This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medical Sciences) of the AAAS and the North American Regions of the Biometric Society, and supported by grant BMS 75-0280) from the National Science Foundation. What follows in this volume are papers by nine of the participants who not only felt that they had something to say in a symposium entitled, "Contributions of Mathematical Models to Biological Discovery," but who falso were willing to record their ideas in more detail here."