We highlight this need for the following reasons:
In general Australia possesses a sound research base although certain sub-disciplines, among them Operations Research and Financial Mathematics, need strengthening. The health of the research base in Australia was plain to see. Among the measures of performance used were bibliometry and the level of funding by the Australian Research Council (ARC).
Australia's mathematicians and statisticians publish about two percent of the world's papers in their discipline. One well-known survey puts the figure at 2.3%, whilst other databases give smaller percentages. These papers were cited about ten percent more than the world-wide average for papers in the discipline. These are impressive figures for a country with a small population. The Mathematical Sciences in Australia enjoy a higher percentage of world output than disciplines like Clinical Medicine, Chemistry, Engineering and Physics.
This level of publication had a slow decline over the 1980s, but the number of citations per paper increased a little. Australia's publication level in statistics was remarkably high, helped by extensive use of statistics in CSIRO for Australia's primary industries for some decades from 1950 onwards.
A second perspective is obtained from ARC funding. Large ARC grants directly classified under the Mathematical Sciences were 1.7% of the total in 1987, 2.8% in 1991, and 3.7% in 1993. ARC grants represent world-class performance. There is intense competition for them, and in recent years the success rate for applications is about 20%. The ARC grants reveal another astonishing feature--the pervasiveness of the Mathematical Sciences--but more about that later.
The Mathematical Sciences are generic and enabling technologies.
They are essential to the prosperity of many value-adding industries
in Australia.
We found unequivocal evidence of the value of the Mathematical Sciences to Australia. Applications were identified across all industry sectors. Notable examples cited within the review include defence, mining, mineral-processing, services and manufacturing. Within any particular industry sector, the Mathematical Sciences are used at all stages of a value-added chain.
The mining and mineral-processing sector is an example with a distinctly Australian flavour. Table 1 below, reproduced from the review, indicates the significant need for the Mathematical Sciences within this industry.
In the report we described an example where the Mathematical Sciences had a large financial impact. This was work carried out by my colleagues in Division of Mathematics and Statistics for the Electricity Trust of South Australia. Box 3.4 of that report[ 1] describes this work--on risk management of assets--which will lead to savings of up to $250 million.
The importance of this contribution needs further emphasis because:
It is well-known that the Mathematical Sciences are widely used in other disciplines. What was surprising was the extent to which this takes place. To illustrate this finding in the university context, we turn once again to publishing output and ARC data.
Over half of the published output of Mathematical Sciences departments appears in journals for other disciplines. For Physics, Chemistry, the Earth Sciences and Biology, the comparable figure is about one quarter.
We also found that many ARC Large Grants were either (a) given to members of Mathematical Sciences departments, but classified under other disciplines; or (b) given to applicants in other disciplines, but on topics that were clearly mathematical in nature. Altogether these two categories amounted for nearly twice as much as those grants directly classified under the Mathematical Sciences.
We also found an extraordinary pervasiveness in the case of advanced mathematical services. The Mathematical Sciences were applied in every industry sector examined. Typically the Mathematical Sciences played a key and central rôle. Often the use of the Mathematical Sciences was not evident to the user, who used a software product having a fanciful graphical user-interface which masked the underlying mathematical concepts and algorithms.
A wonderful example of this is in yield-management for airlines, in which notions from the Mathematical Sciences are used to optimise the number of passengers paying full fares. The next time you make an airline booking, remember that you will be ``flying in yield-management cyberspace under the control of mathematical models using dynamic-programming, linear-programming, exponential-smoothing and other tools of optimization and estimation''. Have a nice trip!
Amongst these challenges we specifically identify:
If these challenges are not addressed successfully there will be significant diminution in Australia's capabilities in the Mathematical Sciences, to the detriment of the nation.
These limitations show the Mathematical Sciences have a lower profile than they should. Other factors which also need to be addressed include the gender imbalance of the discipline, the narrowness of its funding base, and its skewed age-distribution.
Each of the 20 recommendations in the report were made with the long term benefits of the profession in mind. Professional mathematical scientists might be disappointed that we make no particular recommendations concerning ARC Large Grants. Most however, will enthusiastically endorse the recommendations which call for a Special Research Centre and a Cooperative Research Centre in the Mathematical Sciences.
To conclude, this Review involved wide consultation and was developed with a broad consensus. I urge researchers and practitioners to support the recommendations for the benefit of the profession.