The developments in technology to increase the throughput of experiments in the biosciences has led to an explosion in data generation and a pressing need to find ways to make sense of that data. The advent of “Systems Biology” and “Computational Biology” has shone a spotlight on mathematical approaches and revealed some weakening cracks in the ability of biologists to understand the mathematics and the ability of those with mathematical skill and insight to communicate their ideas and results.
The importance of mathematical approaches is expressed very elegantly in Joel Cohen’s essay title:
Mathematics Is Biology’s Next Microscope, Only Better; Biology Is Mathematics’ Next Physics, Only Better.
Joel E. Cohen, PLoS Biol. 2004 December; 2(12): e439
The analogy is very powerful as Cohen comments:
The discovery of the microscope in the late 17th century caused a revolution in biology by revealing otherwise invisible and previously unsuspected worlds.
And it is backed up with an array of fascinating examples where mathematics has had an impact upon biology from William Harvey’s analysis of blood circulation in 1628, through the Logistic equation for limited population growth (Verhulst in 1838), Pearson’s correlation coefficient, Markov’s chains, Fisher’s ANOVA, to the effect of dogs on the transmission of Chagas’ disease in Argentina (2001).
Cohen’s argument is that those with some experience of, and insight into, mathematics can see things differently and with greater clarity.
Charles Darwin was right when he wrote that people with an understanding “of the great leading principles of mathematics… seem to have an extra sense” (F. Darwin 1905).
It is these principles of mathematics, rather than just the algebra-crunching and number-crunching that matter. It is like putting on a special pair of glasses to watch a 3D movie:
Those who understand the calculus, ordinary and partial differential equations, and probability theory have a way of seeing and understanding the world, including the biological world, that is unavailable to those who do not.
This is a compelling argument for ensuring that all biological sciences students undertake some study of mathematics (not only statistics) within a biological context. The main advances in mathematics education within bioscience degree programmes, in the UK at least, has been the realisation of the importance of context. The mathematics needs to be presented within the biological context and assessed to sufficient depth. Relying upon school mathematics, even to A level standard, is usually not enough, but more of that another time.
Cohen’s argument rests the responsibility of understanding the mathematical approaches largely upon the biologist and bioscience education and this is where I beg to differ. How many times have I attended a mathematical biology seminar (as a biologist not a mathematician) and found people speaking in another language. It seems once a mathematician learns the mathematical language they forget how to speak in English. I suggest that we need to spend considerable effort thinking about how to communicate the output of mathematical biology / systems biology / computational biology. Perhaps we need to work from both ends of the spectrum.