What has mathematics done for biology?

Abstract

“Whathasmathematicsdoneforbiology?”isaquestionthateverymathematicalbiol-ogisthasbeenaskedatsometime,orhasaskedthemselves.Whilebioinformaticshasbeen very successful and widely accepted in biology, the acceptance of mathematicalbiology has been slower. Of course, there are notable exceptions—in ecology andepidemiology there is a long history of mathematical modelling [see, e.g., the booksby 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)], whilein pattern formation the Turing model (Turing 1952), while still controversial, hascertainlystimulatedanenormousamountofexperimentalactivityandledtothepara-digm patterning principle of short-range activation, long-range inhibition (Gierer andMeinhardt 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 past50years. In fact, during the past 20years bioinformatics has come into being andtaken over mathematical biology in the race to the laboratory. There are a number ofreasonsforthis:(1)therehavebeenfewmajorproblemsthatmathematicalbiologyhassuccessfullyaddressed(comparedwiththegenomeproject),(2)forvalidation,modelsinmathematicalbiologytypicallyrelyonspatiotemporallyresolveddataand,todate,datatendtobestatic(electrophysiologyisanexception)andthereforemoreamenableto the tools of bioinformatics. However, mathematical biology has made numerousadvancesinbiology,andadvancesintechnology(particularlyimaging)areleadingto