It will be explained how the following problems in the diagnosis and treatment of breast cancer have led to mathematical problems: 1. How can one improve the diagnosis of breast cancer? 2. How can one determine the growth rate of a cancer once it has been detected? 3. In which order should drugs be given in order to improve relapse and survival times? The first problem led to the design , construction, and testing of an electrical impedance spectroscopy system combined with an x- ray mammography system. The second problem led to a quantitative model to predict the growth rate of some cancers as a function of the number of Her2 and EGF receptors on the cells involved. The third problem led to quantitative models capable of predicting the outcome of specific chemotherapy regimens used by Bonadonna involving the use of CMF and A (Doxorubicin) for the adjuvant treatment of breast cancer.