Further Applications of Mathematics in the Natural Sciences

In this chapter I would like to give some additional examples of sophisticated mathematics used by physicists and biologists today. There are situations where classical mathematics, the solution of differential equations, which describe physical phenomena, are not obtainable in a closed form by the methods of standard analysis. A lot of numerical work of heuristic value was done in Los Alamos during and after World War II, and this is perhaps a novel feature of present day applications of mathematics, but the physicists there also used some very abstract mathematics. For example, some results of topology were of use in the design of accelerators.