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 nonlinear 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:
 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.
 Reaction diffusion equations  the field of nonlinear 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 nonlinear reaction diffusion equation (with a logistic
term for the growth component) is called Fisher's equation.
 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.
 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 online in:
 Levin,
S. A. (ed.). 1992. Mathematics and Biology: The Interface 
Challenges and Opportunities. Lawrence Berkeley Lab PUB701


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

Mathematical Modeling in Biology Texts
