What has mathematics done for biology?

“What has mathematics done for biology?” is a question that every mathematical biologist has been asked at some time, or has asked themselves. While bioinformatics has been very successful and widely accepted in biology, the acceptance of mathematical biology has been slower. Of course, there are notable exceptions—in ecology and epidemiology there is a long history of mathematical modelling [see, e.g., the books by Murray (2002, 2003) and May and McLean (2007)], in physiology the Hodgkin– Huxley model is well known [see, e.g., the book by Keener and Sneyd (2009)], while in pattern formation the Turing model (Turing 1952), while still controversial, has certainly stimulated an enormous amount of experimental activity and led to the paradigm patterning principle of short-range activation, long-range inhibition (Gierer and Meinhardt 1972). These successes for mathematical biology are significant, but still relatively rare, bearing in mind that the field has matured and grown substantially over the past 50years. In fact, during the past 20years bioinformatics has come into being and taken over mathematical biology in the race to the laboratory. There are a number of reasons for this: (1) there have been fewmajor problems that mathematical biology has successfully addressed (compared with the genome project), (2) for validation, models in mathematical biology typically rely on spatiotemporally resolved data and, to date, data tend to be static (electrophysiology is an exception) and therefore more amenable to the tools of bioinformatics. However, mathematical biology has made numerous advances in biology, and advances in technology (particularly imaging) are leading to