Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models, and abstractions of living organisms to investigate the principles that govern the structure, development, and behavior of the systems. In contrast, experimental biology involves the conduction of experiments to test scientific theories. The field is sometimes called mathematical biology or biomathematics to emphasize the mathematical aspect, or as theoretical biology to highlight the biological aspect. Theoretical biology focuses more on the development of theoretical principles for biology, while mathematical biology focuses on the application of mathematical tools to study biological systems. However, these terms are often used interchangeably, merging into the concept of Artificial Immune Systems of Amorphous Computation.
Mathematical biology aims at the mathematical representation and modeling of biological processes, using techniques and tools of applied mathematics. It can be useful in both theoretical and practical research. Describing systems in a quantitative manner means their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter; requiring mathematical models.