When preparing this submission, I discovered that many of my prime concerns and suggestions re Australian mathematics have already been expressed cogently and succinctly in documents such as “A National Strategy for the Mathematical Sciences in Australia” (National Committee for Mathematical Sciences, AAS, Mar 2009), and the Forum Communique of AMSI’s “Maths for the Future” forum of 7-8 Feb 2012. So I shall make this document briefer by simply emphasizing my strong support for certain parts of these documents.
In particular, I have strong support for (primary themes: national public awareness (this should be a theme in its own right!), and mathematics school education):
1. The second recommendation of the 2012 AMSI Forum (“A five-year national awareness campaign for mathematics and statistics targeting both the school and higher education sectors and the general public. …” (emphasis added). I strongly support the entire recommendation.) (The government implemented the first recommendation.) My view is that AMSI (taking advice from the AMS and the Academy’s maths committee) is probably the best organization to supervise and support such an awareness campaign. However I believe that the main effort will have to come from Australia’s individual professional mathematicians (ie us), largely through volunteer effort at both local (eg individual schools) and national (eg public talks, newspaper articles, TV interviews & commentary) levels. The latter requires relatively rare, but not non-existent, communication skills.
In fact I have strong support for the views expressed in the entire Forum Communique, which cover the critical need for “suitably trained mathematics teachers”, a serious concern over falling enrolments in intermediate and advanced year 12 mathematics, that (in Australia) “demand for high-level mathematical skills far outstrips supply”, and the need for us to “work together to communicate the importance of our discipline to the Australian public”. However I think that we will have to supply most of the effort in this “communication of importance”, probably with little funding support.
The virtually unanimous support of the Australia mathematics community (as expressed by a wide range of representatives at the AMSI Forum) for these views is echoed (relative to physics education and public appreciation) in the recently released Physics Decadal Plan. This suggests the two communities could work productively together in these respects.
2. Most of the 2009 National Strategy, in particular most of section 4 “Our Solutions”. To my untrained eye, the two page 2012 Forum Communique approximates a summary of the 11 page 2009 National Strategy, with the latter having significant supporting data for its arguments. This document, and the AMSI Forum, highlighted how UK actions over about the last decade have reversed the decline in high school student numbers taking advanced maths courses.
I also have some comments on other themes for the Decadal Plan.
3. Research Centres in mathematics & statistics: 3. best models for our purposes. I support the establishment of a national mathematics research centre. It seems to me that such research centres, due, for example, to sponsoring “special years” on mathematical/statistical research areas internationally viewed as having great current promise, and having a “critical mass” of researchers in relevant areas, can enormously contribute to the health and dynamism of the research community, and of “putting Australia on the map” of international mathematics / statistics research. However funding for such a centre should not reduce available ARC funding for individual researchers. Due to lack of current familiarity with “world’s best practice” in the structure of such centres, I won’t specify a particular model.
4. Mathematics / statistics research in universities: 2. Breadth & depth. The maths community needs to have continuing confidence there are systems in place to ensure appropriate support for innovative, high-quality research by beginning mathematicians. Here I am thinking of research in areas beginning to be recognized internationally as particularly exciting and of great potential, but in which there is no current research (and possibly no awareness) by established Australian mathematicians.
5. Mathematics / statistics research in universities: 4. interdisciplinary. I believe we need to work towards wider awareness of, and appreciation for, mathematics, across university science, engineering and medicine (& other?) research disciplines. One idea might be that the university maths community do outreach to the rest of university – “maths appreciation days”. The aim would be to solicit and encourage suggestions and requests for maths support from the rest of the university research community, and to establish contacts facilitating multi-disciplinary collaboration.
6. Mathematics / statistics research in universities: 1. PhD programs. Mathematics PhD courses. Possibly due to my own experience and conservatism, I prefer the current structure of 4 year honours, followed with a PhD, rather than a 3 year degree, then 2 year masters, then PhD. I think we must supply a year’s worth of quality and appropriate graduate courses at the beginning of the PhD, comparable to US practice. However technology is progressing rapidly, and I would expect many of these courses could be supplied by the MOOC model (with nationally coordinated assessment?), together with national courses delivered via Access Grid. Others could be provided as now by the home university and AMSI summer schools.
7. Mathematics in industry: 1. Training; 2. Research; 3. Linkages. I believe that we should continue and preferably expand MISG type activities.
8. Mathematics & statistics in government instrumentalities: 1. describing the value. (DSTO). A few years ago, Peter Hall told me he believed that NSA was the largest employer of PhD mathematicians in the US. While I have no idea whether this is true, it is certainly true that mathematics, especially theoretical mathematics (including but not limited to abstract algebra, discrete maths, number theory, combinatorics, probability theory) and certain areas of applied mathematics (such as statistics (I hope the statisticians will pardon this!), high performance computing skills, algorithmic maths, big data analysis) are critical for the national effort in information security and intelligence.
A number of mathematicians in the Department of Defence are involved in school outreach, eg the CSIRO managed Mathematicians in Schools program, supported by DSTO. Another is the DSD Information Security Hub (DISH).
This is a personal submission and should not be taken to have any endorsement by my employer, nor to reflect their views.