Mathematics is a great enabling discipline underpinning science, engineering and technology. The modern society, more than ever, relies on mathematics to function. Mathematics differs essentially from many other disciplines in that it has no *use-by date*. Mathematical discoveries of Archimedes, Galileo, Newton and Gauss are just as correct today as they were at the time of their discovery. New mathematical advances do not destroy, or discredit, existing results. Rather they build on these results providing new insights, capabilities and, ultimately, new technologies. It is, perhaps, because of the continuity of mathematical research that some things within the *world of mathematics *do not change. Among the latter is the fact that, as throughout history, there are two main drivers of mathematical research and innovation. These are:

- difficult open problems that fascinate great mathematical minds, and
- the
*big questions*related to the current challenges that human societies are facing.

These two drivers of mathematical progress co-exist and reinforce one another. For instance, when faced with a threat of imminent German invasion of their country, Polish mathematicians built a working replica of the now famous “enigma” machine for encoding messages. The machine was delivered to the British researchers at Bletchley Park just in time and, in the process, planted the seeds of the modern mathematical topic of cryptography that has led to advances in number theory and algebra. In any case, at a very fundamental level, these two drivers of mathematical research lie at the heart of the differentiation that some researchers make between applied and pure mathematics.

By acknowledging the essential dichotomy of mathematics we in FMSL recognise that for mathematics to flourish as a discipline - in a sustainable way - we must pursue excellence in both modern applied and pure mathematics. On the one hand the new fundamental theories of pure mathematics are often inspired by the common threads of diverse applied mathematical models. On the other hand applied mathematics relies on the translation of new theories to an application context where they are realised.

In view of this, FMSL's research focus is:

Advances in modern applied and pure mathematics and their nexus.

This is captured in the motto:

A theory is in applications revealed and applications are in a theory concealed.

By addressing problems that have challenged top mathematicians, engineers and computer scientists FMSL mathematicians focus their research on projects that directly address the Australian Research Council's research priority Frontier Technologies for Building and Transforming Australian Industries, in particular their priority goals 'Breakthrough science' and 'Frontier technologies'.

## Research programs

Currently, FMSL houses five focused research concentrations that reflect our areas of existing and growing research strengths.

Each of these areas has a recognised research leader and research outputs. While the majority of contributing researchers are from CSEM some come from other Flinders research units, such as School of the Environment, Faculty of Medicine, Nursing and Health Sciences and the National Centre for Groundwater Research and Training, where mathematical research is also utilised extensively.

- Analysis
- Biomedical Mathematics
- Continuum Modelling and Environmental Applications
- Discrete Mathematics, Optimisation and Operations Research
- Statistics and Stochastic Modelling

## Further information

We would be happy to provide more information about the School's research programs, the opportunities for higher degree study and scholarship information.

For more information, please contact the Laboratory Director - Associate Professor Vladimir Ejov - or the coordinators of the research program you are interested in.