Ian Stewart:

Biology used to be about plants, animals and insects, but five great revolutions have changed the way that scientists think about life: the invention of the microscope, the systematic classification of the planet’s living creatures, evolution, the discovery of the gene and the structure of DNA. Now, a sixth is on its way – mathematics.
Maths has played a leading role in the physical sciences for centuries, but in the life sciences it was little more than a bit player, a routine tool for analysing data. However, it is moving towards centre stage, providing new understanding of the complex processes of life.
The ideas involved are varied and novel; they range from pattern formation to chaos theory. They are helping us to understand not just what life is made from, but how it works, on every scale from molecules to the entire planet – and possibly beyond.
The biggest revolution in modern biology was the discovery of the molecular structure of DNA, which turned genetics into a branch of chemistry, centred on a creature’s genes – sequences of DNA code that specify the proteins from which the gene is made. But when attention shifted to what genes do in an organism, the true depth of the problem of life became ever more apparent. Listing the proteins that make up a cat does not tell us everything we want to know about cats.