In the 1980s Australia published 2.3% of the world's papers in Mathematics. These papers were cited 10% more than the world-wide average. This research-base enables us to adapt overseas developments for local usage. For example, our local research-base supports indigenous cryptographic work to the extent that ``the national security depends on crypto-mathematical advice''.
The Mathematical Sciences make significant contributions to Australia's prosperity from all sectors of the economy. Within particular sectors the Mathematical Sciences are needed at each step of a value-adding process. To give an important Australian example, I'll show how the Mathematical Sciences are used in mining and mineral-processing--right from exploration, ore-body estimation, excavation, transportation, beneficiation, smelting, all the way through to elaborately transformed products.
A striking feature is the pervasiveness of the Mathematical Sciences. Over half of the publication output of Mathematical Sciences departments appears in journals for other disciplines. Of the grants made by the Australian Research Council for work that is clearly mathematical in nature, well over half were awarded to researchers in other areas including physics, engineering and economics. The Mathematical Sciences are essential to the work of many Cooperative Research Centres (CRC), despite the fact that no CRC is dedicated to this, the most generic of disciplines.
But why the iceberg analogy? And what negative aspects did we identify? Well, the Mathematical Sciences certainly do have a low profile. They are seen as being hard, unattractive to students and more suited to males than females. The age-distribution of academic mathematicians has a pronounced bias. Finally, Mathematical Sciences in Australia have a narrow funding-base; mechanisms for technology-transfer need to be boosted.