The below is derived from a brief response to an email question from an undergraduate math major who wished to know how biology has contributed to mathematics.

You asked about how biology affects math. There are many mathematicians doing what amounts to research in math that is motivated by biological examples. Many of the research papers that appear in journals such as the Journal of Mathematical Biology and Mathematical Biosciences are creating new math, but are motivated by some underlying biological problem. Indeed, some people would argue that virtually all of the research in non-linear dynamical systems has historically been motivated by biological (viewed in a broad context to include human health and social interactions) questions. I will give you four examples of fields of mathematics that have been developed in part due to the biological underpinnings:

1. Chaos theory - the first papers to bring out the possibility of chaos arising in simple discrete difference equations were written by Bob May (Sir Robert May, FRS, the Science Advisor to the British Government) in the early 1970's. These papers showed how a simple population model (the discrete logistic) could give rise to very complex dynamical behavior.

2. Reaction diffusion equations - the field of non-linear reaction (growth terms) in parabolic partial differential equations with diffusion is inherently linked to the early efforts of R. A. Fisher and Sewall Wright to develop the theory of population genetics. Indeed, the canonical non-linear reaction diffusion equation (with a logistic term for the growth component) is called Fisher's equation.

3. Genetic algorithms - this entire approach to optimization problems in hosts of different fields arises as a direct attempt to mimic the forces of natural selection by generating variants, selecting among them by a "fitness" criteria, and letting the system evolve.

4. Neural nets - again, this approach derives from attempting to mimic the learning which arises in neurobiology from connected networks of neurons.

More information about these matters may be found on-line in:

Levin, S. A. (ed.). 1992. Mathematics and Biology: The Interface - Challenges and Opportunities. Lawrence Berkeley Lab PUB-701

 

I have a list of books dealing with mathematics and biology on my home page at:

Mathematical Modeling in Biology Texts

Mathematics Awareness Month is sponsored each year by the Joint Policy Board for Mathematics to recognize the importance of mathematics through written materials and an accompanying poster that highlight mathematical developments and applications in a particular area.