According to Ian Stewart (“The formula of life,” *New Statesman*, 27 April 2011),

Biology is undergoing a renaissance as scientists apply mathematical ideas to old theory. Welcome to the discipline of biomathematics, with its visions of spherical cows, football-shaped viruses and equations that can predict the pattern of a zebra’s stripes.

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.

What will this mean? That math will get upgraded from a “bit player” to “centre stage” in biology, says Stewart:

The classical geometry of Euclid is formulated in two dimensions (the plane) or three (space). The shapes of viruses lead to something less familiar: geometry in six dimensions. I am not suggesting that viruses come from the sixth dimension – that might make a good title for a sci-fi movie, but little more. However, the mathematics of six dimensions turns out to be a good way to understand viruses in three dimensions, because the complicated three-dimensional shapes observed in viruses turn out to be “shadows” or slices of simpler, six-dimensional shapes.

The climax of Euclid’s classic geometry text, the Elements, identifies five regular solids: cube, tetrahedron, octahedron, dodecahedron and icosahedron. The names, cube aside, refer to the number of faces: four, six, eight, 12 and 20, respectively. The cube has square faces, the dodecahedron has pentagonal ones, and the other three are made from equilateral triangles.

Euclid’s elegant icosahedron, devoid of practical application for more than 2,000 years, turned out to be just the right shape for making a virus. The big question was: why? Part of the answer is energy.

This sounds more like design or self-organization than like natural selection acting on random mutation. Sure enough:

Yet something isn’t right here. The principle of competitive exclusion, introduced in 1932 by the Russian biologist Georgii Gause, states that the number of species in any environment should be no more than the number of available “niches”, or ways to make a living. If two species try to compete for the same niche, then natural selection implies that one of them should win. This is the paradox of the plankton: the niches are few, yet the diversity is enormous – many thousands of species. The solution to the paradox comes from chaos theory.