Needs for the Future: Radically Different Types of Mathematical Models

Abstract

Since parts of future biomathematics which involve further development along directions already predominant can be extrapolated from the other papers in the volume, the purpose of this paper is to investigate less obvious, and therefore more speculative, directions. In particular, I intend to show reason to suspect that the laws of biology are of a different mathematical form than the laws of physics and that, therefore, the mathematical models of the future in biology will be radically different from the models used in physics. I will primarily concentrate on casting doubt on the ultimate usefulness of many differential equations models by examining the extent to which the mathematical assumptions underlying these models reflect biological reality. Since these mathematical assumptions seem to be seriously discordant with important parts of biological reality, this type of mathematical model should ultimately be replaced by essentially different types of mathematical models.