Processes and Problems That May Define the New BioMathematics Field

Historically, mathematics developed hand-in-hand with the physical sciences. While biological processes must obey the laws of physics, biology is not reducible to physics (otherwise we would not be able to distinguish one set of phenomena from the other!), and therefore mathematics that have been adequate for describing physical processes are often inadequate to describe biological ones. In consequence, I argue that the a new phase of scientific development is required in which mathematicians turn to biological processes for inspiration in creating novel forms of mathematics appropriate to describe biological functions in a more useful manner than has been done so far. Many the kinds of problems that seem to remain unaddressable at present involve forms of mathematics that currently have competing assumptions. For example, biologists need to describe phenomena that involve discrete and continuous functions simultaneously (control of metabolism through binding of single molecules to unique gene promoters; the statistical description of continuously varying molecular complexes); they need to handle spatial descriptors (geometry?) at the same time as kinetic data (calculus?) to explain developmental processes; they need to explain how scalar processes (random diffusion) gave rise to vectorial ones (facilitated transport). These, and other hybrid problems described in this paper, suggest that a fertile field of enquiry exists for mathematicians interested in developing new forms of biologically-inspired mathematics. I predict the result of the development of this new field of biologically-inspired mathematics will be as fundamentally revolutionary as physics-inspired mathematics was during the original Scientific Revolution.