Some Remarks on Applied Mathematics

Encourage students to focus on fundamentals. In mathematics this means algebra, analysis and geometry, but it is also desirable for an applied mathematician to have a broad education in science and engineering, including the perspectives found in computer science. It is impossible to predict what kinds of mathematics will be especially useful for the problems yet to be encountered. Being prepared to read about the work of others and having a first hand knowledge of many good examples is about the best one can do. One of the very positive side effects associated with the increasing number of scientifically and mathematically literate people in the world is that there are now readable books and survey papers covering a vast array of scientific work. It is essential that students who aspire to be model builders and problem solvers should have the tools necessary to make use of this resource. This point is well illustrated by recent developments in mathematical physics involving the use of some of the very latest ideas in geometry to provide a language suitable for unifying field theories.