Robert May is one of the world’s leading mathematical biologists. He is President of the Royal Society (only the second Australian in its 350-year history) and a Professor of Zoology at Oxford University and Imperial College.

    He was Chief Scientific Advisor to the UK government from 1995-2000. In 1996 the Royal Swedish Academy awarded him The Crafoord Prize (the equivalent of a Nobel Prize) for his pioneering ecological work into the theoretical analysis of the dynamics of populations, communities and ecosystems. The Royal Swedish Academy described his influence on contemporary ecological research as ‘quite overwhelming.’

The Journal Science invited May to contribute to its Special Section (February 6, 2004) on Mathematics in Biology. He titled his paper "Uses and Abuses of Mathematics in Biology" which might have carried the subtitle, It pays to know what you're doing. He opens with:

In the physical sciences, mathematical theory and experimental investigation have always marched together. Mathematics has been less intrusive in the life sciences, possibly because they have until recently been largely descriptive, lacking the invariance principles and fundamental natural constants of physics. Increasingly in recent decades, however, mathematics has become pervasive in biology, taking many different forms: statistics in experimental design; pattern seeking in bioinformatics; models in evolution, ecology, and epidemiology; and much else. I offer an opinionated overview of such uses – and abuses.

And he immediately cites a telling example of the price of ignorance. Darwin "thought that inheritance 'blended' maternal and paternal characteristics. However, as pointed out to Darwin by the engineer Fleeming Jenkin and others, with blending inheritance it is virtually impossible to preserve the natural variation within populations that is both observed and essential to his theory of how evolution works." May concludes that if Darwin had grasped the mathematical significance of Mendel's results demonstrating particulate inheritance, Jenkin's objection would have been resolved. That had to wait half a century.

    To cite a positive case Around 1940 Max Delbrück, AD Hershey and SE Luria began studying bacteriophage, a type of virus that infects bacteria. Their object was to find a living system as simple as possible, on which to study fundamental life processes, starting with self-replication. They followed what happened during infection in single bacteria and analysed their results with advanced statistical methods.

    They made a series of fundamental discoveries for which they were awarded the 1969 Nobel Prize for Medicine or Physiology. A matter of key importance was Delbrück's training as a physicist (like May) who became interested in biological problems. In fact in the early 1930s Delbrück's collaboration on mutational analyses in the fruit fly Drosophila led to a quantum-mechanical model of the gene, permitting, for example, estimations of gene size.

    Currently many nation's, Australia included, have tended to throttle back support for the enabling sciences and mathematics while fostering biomedical research, an avenue seen by politicians as a better vote getter than promoting the more abstruse disciplines. But as May points out:

...the increasing speed and sophistication and ease of use of computers enables an increasingly large number of life scientists who have no substantial background in mathematics to explore "mathematical models" and draw conclusions about them. Such activity usually consists of representing sensible and evidence-based assumptions as the starting point for a complicated and usually nonlinear dynamical system, assigning particular parameters (often in an arbitrary way), and then letting this complicated system rip. This represents a revolutionary change in such theoretical studies. Until only a decade or two ago, anyone pursuing this kind of activity had to have a solid grounding in mathematics. And that meant that such studies were done by people who had some idea, at an intuitive level, of how the original assumptions related to the emerging graphical display or other conclusions on their computer. Removing this link means that we arguably are seeing an increasingly large body of work in which sweeping conclusions – "emergent phenomena" – are drawn from the alleged working of a mathematical model, without clear understanding of what is actually going on. I think this can be worrying

    Unless the trend of reducing support for mathematics and the enabling sciences is reversed, Australian research in the life sciences in general and biomedical research in particular will decline in its contribution to the nation's well being. It is all very well to speak of interdisciplinary research, but unless there is a firm foundation in mathematics, physics and chemistry in our universities and most importantly in our major research universities talk of interdisciplinary research will be just that – so much talk.

Alex Reisner

The Funneled Web