On Growth and Forms** is one of the most original scientific works produced in the 20 th century. Its author, the British biologist and mathematician D'Arcy Thompson, displays his vast knowledge of the classics in the service of an intellectual project aimed at placing mathematics at the heart of the study of living organisms.
When he embarked on this task, Charles Darwin's theory of evolution was still the subject of much debate, though its general principles had by then gained broad acceptance within the scientific community. Darwinism, which had yet to develop into the modern synthesis we know today, holds that the random mutations occurring in members of a species amount to involuntary "trials": often unsuccessful or without effect, but sometimes beneficial to the species' survival in its environment. A kind of "optimization by trial and error," this mechanism explains transformations in the living world without having to invoke outside intervention, particularly divine intervention.
Quantifying evolution
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Elegant though it is, this idea of the "survival of the fittest" remains largely qualitative and leaves an obvious question unanswered: how do we define "the fittest"? One important part of the answer is that there is no definition in abstracto: everything depends on the environment in which the species evolves. The conditions best suited to survival at the poles, for example, are not the same as in a temperate region.
D'Arcy Thompson tried a different approach, seeking to avoid the pitfall of defining "the fittest" simply as... those that survive. He looked to mathematics for a criterion for selection external to the environment, one less closely tied to it.
