Picture this: A theoretical biologist out for a mountain hike meets a sleeping shepherd. The shepherd awakes visibly disturbed. He offers the theoretical biologist one of his sheep as a reward if he is able to calculate the exact number of animals in his herd. The theoretical biologist estimates the number to perfection and goes to take his prize. To the shepherd's amazement, the theoretical biologist fails to recognise that he has unwittingly picked the shepherd's dog instead of a sheep. This story often relayed as a joke quite nicely sums up a common prejudice, but it also expresses some truths about theoretical and mathematical biology. The strength of biomathematics lies in the calculation of specific values and also in the identification of common structures and patterns at different levels of biological organisation--but not the necessarily biological differences per se.

Today theoretical/mathematical biology is booming; currently it seems to offer lots of promising perspectives and possibilities for mathematicians and theoretically interested biologists. The establishment of many new institutes, curricula, and research networks at the European level reflects this surge of interest; take, for example, the currently launched EU Marie Curie network, ''Modelling, Mathematical Methods and Computer Simulation of Tumour Growth and Therapy." But such a boom raises suspicions: Is this a fad? Or does mathematical biology offer solid long-term perspectives?

The contemporary "data jungle", which stems mainly from newly available molecular biology methods and the development of computer processing capabilities, is responsible for the more recent boom in mathematical biology. As the 20th century was the ''century of physics,'' the new century may well be the ''century of biology," although this is of course difficult to state so early on in the century as 2004!

A rich European history

It may come as surprise to some that mathematical/theoretical biology is nothing new. There are Baltic, British, French, German, Italian, and Russian roots going back as far as the late 19th century. The need for theoretical biology methods was strongly spurred by the enormous amounts of new data arising from the scientific observations of the time (e.g., from expeditions into colonial countries) and new emerging experimental techniques. The famous experiments of Mendel, and the fruitful communication between experimental biologists and applied mathematicians in the 1930s, marked the beginnings of population genetics and were seminal for biomathematics. As early as 1896, British professor K. Person applied the now standard statistical techniques of probability curves and regression lines to genetic data. This was seemingly the first proof of the existence of a mathematical law for biological events.

Together with specialties from related disciplines such as bioinformatics and biophysics, mathematical methods are applied increasingly to biological systems. Rather new and hot applications lie in the fields of bioengineering, developmental biology, immunology, infectious diseases, and tumour therapy. Apart from the need to develop particular models for highly specialized biological and medical problems, mathematical biology helps to identify common patterns, e.g., to extract general principles from complex systems. A better understanding of such principles can then be exploited for technological applications; see for example the European RTD project BISON (Biology-inspired techniques for self-organization in dynamic networks).

Institutional support for math-biology interdisciplinarity is still developing. When I started my undergraduate studies in mathematics at the University of Mainz, Germany, in the 1980s, special permission was required to get biology accepted as a minor subject. In those days the common minor subjects were physics and economics. Already during school days, I had been interested both in mathematics and biology. So what were my options? I consulted a professor of biology who advised me to concentrate on a pure mathematical degree and get into biology later, for example, through a Ph.D.

This turned out to be very good advice, and it is still applicable today. Whereas biology has a modular structure--different areas such as cell biology, evolution, or ecology can be studied quite independently of each other--mathematics follows a sequential order and is accumulative. One needs an introduction to such basics as analysis, linear algebra, and numerical analysis before one can proceed with advanced topics like differential equations or stochastics. I would recommend finishing a math master's degree, and there are now possibilities to specialize in biomathematics (in Germany, e.g., at the Universities of Bonn and Greifswald and Humboldt University in Berlin).

Personal journey through mathematics and biology

In my master's thesis I developed a coding scheme for bank computers based on so-called linear shift registers. My supervisor was Prof. A. Beutelspacher. His lectures offered an enormous intellectual pleasure because he tried to communicate mathematical ideas in an understandable way; he clearly had a ''mathematical mission''. Prof. Beutelspacher recently opened the successful Mathematics Museum in Giessen.

For my Ph.D. I went to the University of Bremen, where I discovered my interest in natural patterns while designing experiments and mathematical models of striking patterns of fungal growth under the supervision of cell biologist Prof. L. Rensing and mathematician Prof. A. Dress. It became clear that doing 'wet experiments' and 'dry modelling' was not feasible in the long-term perspective because both aspects of the (inter)discipline are highly demanding.

So I moved to the theoretical biology group of Prof. W. Alt at the University of Bonn and concentrated on the development and analysis of models for interacting cell systems; examples of interacting cell systems are growing microorganisms or tumours. I finished my habilitation on ''Cellular Automation Modelling of Biological Pattern Formation'' at the University of Bonn.

After a fruitful intermezzo spent at the Max Planck Institute for the Physics of Complex Systems in Dresden, I became head of the new department there--Methods of Innovative Computing at the Centre for High Performance Computing, led by Prof. W. E. Nagel, at the Technical University Dresden. My research group is trying to develop and analyse mathematical models, algorithms, and simulations in close co-operation with experimentalists and medical doctors.

To work in mathematical biology, one needs to be able to identify biological problems that can be tackled with mathematical methods. In practise this means to choose or develop an appropriate mathematical structure; this is the modelling part. Interpretation of the results has to be carried out in close contact with the experimentalist. What is required, and is harder to define, is a ''feeling for biological problems'' in the first place. Communication skills of course play a critical role when working in such an interdisciplinary field.

Growing European support

Given the enormous amount of biological data that already exists and that is likely to be created soon, it seems that there is enough work out there for mathematical biologists over the next decades. Academic career perspectives are promising since interdisciplinarity is strongly supported by major research programmes at the European and national level (e.g., the BMBF Systemology initiative). Industrial career perspectives are still limited but are expected to grow in the future.

MTBio (Network for Modelling and Theory in the Biosciences) is a German network that organises conferences, curricula, and schools and disseminates information on open positions. On a pan-European level, there is the European Society for Mathematical and Theoretical Biology (ESMTB). The society was founded in 1991 and is a nonprofit organisation that promotes theoretical approaches and mathematical tools in the life sciences in a European and wider context. This goal is achieved by organisation of schools and conferences. Communication of the society's activities can be found both online and through the publication of the European Communications (both also have details on further ESMTB activities). There are attractive reductions in fees for ESMTB student members; please see the Web site for details.

An excellent international opportunity to meet people active in the field will be the next conference organised by ESMTB--the European Conference on Mathematical and Theoretical Biology (ECMTB05), which will be held in Dresden, Germany, 18 to 22 July 2005. Also of special interest to young researchers is that ECMTB05 will have a mentoring programme that aims to help newcomers in the field have easier contact with specialists.