Genetics

Abstract

Genetics continues to be one of the outstanding applications of mathematics in the life sciences. Mathematical research has benefited from this interaction by being motivated to create mathematical structures that describe randomness in ways that are used to interpret data and to predict experimental outcomes. Our understanding of random processes was greatly enhanced by this interaction. On the other hand, the development of theories for random processes and the derivation of statistical methods to link them to experimental observations have been pivotal in our understanding of how genetic information is transmitted from one generation to the next. These show how genetic structures can be engineered to create important products such as novel drugs, strains of bacteria that degrade toxic waste, and a variety of crops and animals used in agriculture. This fruitful interaction between biology and mathematics has benefited biology with greater understanding of genetics and benefited mathematics with the creation of new structures of random processes and of statistics. As with most mathematical structures, these have found numerous applications elsewhere.