I only arrived in Australia 2 years ago so I probably do not have a proper vision of the country’s mathematical community. It seems to me, however, that pure & applied mathematics are quite separated here. I am not saying that they live in different schools or departments, but there does not seem to have much interaction at the research level between pure & applied mathematics in Australia (or what is called “pure” and “applied” here).
In the country I come from (France), “applied mathematics” covers, for example, computational & numerical analysis as well as theoretical analysis of non-linear PDEs (“à la Trudinger”, if I may say). Moreover, the academic structure formally recognises “pure” and “applied” mathematicians: each academic position has an official label “pure” or “applied”, which plays a role when academics apply for promotions or research leaves for example.
As a consequence, French applied mathematicians are used to live in a community which gathers both very applied and applicable mathematics (e.g. computational techniques for PDEs) and quite theoretical and conceptual analysis (e.g. analysis of non-linear PDEs using measure theory). This results in more interaction between the more applied and more theoretical branches of analysis, for example, and the development of rich mathematical techniques and topics which I find absent from Australia.
I firmly believe that this interaction between pure & applied mathematics should be much more developed/strengthen in Australia, as it will be profitable to both branches. Pure mathematics will find interesting questions to study, with the need to develop a rigorous framework for this study, and applied mathematics will be fed with new theoretical results to develop algorithms and techniques able to bring new solutions to practical problems.
This of course holds at the research level, but should also start from secondary education (and continue in higher education), where students need to be presented with both theoretical mathematical issues and some of their very practical applications. The later must nonetheless not be prominent either, as we need to build strong mathematical foundations in our students before they can becoming excellent applied mathematicians.
PS: in all of this, I include computational & numerical analysis, as well as probability and statistics, in “applied” mathematics (i.e. I am not talking FOR-wise).
