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D'Arcy Thompson combined skills in a way that made him unique. He was a Greek scholar, a naturalist and a mathematician. He was the first biomathematician.
Thompson's father was appointed Professor of Greek at Queen's College (now University College) Galway when D'Arcy was 3 years old but he returned to Edinburgh at the age of 10 to attend Edinburgh Academy. He won the prize for Classics, Greek Testament, Mathematics and Modern Languages in his final year at school. After starting a medicine course at Edinburgh University he changed to study science at Cambridge.
He graduated with a B.A. in Zoology in 1883 but he would not obtain his doctorate until 29 years later in 1923. In 1884 D'Arcy Thompson was appointed Professor of Biology in Dundee (incorporated as part of the University of St Andrews in 1897) and then in 1917 he was appointed to the Chair of Natural History in St Andrews. He was to hold a chair for 64 years, a record which will not now be broken.
D'Arcy combined skills in a way that made him unique. He was a Greek scholar, a naturalist and a mathematician. He was the first biomathematician although he followed in the tradition of another great natural historian with mathematical skills, namely Buffon. His understanding of mathematics was of the modern subject but based on the firm foundations of an understanding of Greek mathematics.
Although he was to write around 300 scientific articles and books all D'Arcy's various skills came together in his most famous book On Growth and Form (1917). This book assumes that all science and learning are one, and attempts to reduce biological phenomena to mathematics. He claimed that all animals and plants could only be understood in terms of pure mathematics.
The shell of Nautilus (shown in the picture above) and the hexagonal cells of the bee's honeycomb related to logarithmic spirals and minimal areas. D'Arcy related such things to the Greek work on approximating 
, 
2 and Euclid's Elements .
D'Arcy Thompson was also a very fine writer and he said
The little gift I have for writing English which I possess, and try and cultivate and use, is, speaking honestly and seriously, the one thing I am a bit proud and vain of - the one and only thing.
At the end of Growth and Form he wrote
... something of the use and beauty of mathematics I think I am able to understand. I know that in the study of material things number, order, and position are the threefold clue to exact knowledge: and that these three, in the mathematician's hands, furnish the first outlines for a sketch of the Universe.
References elsewhere in this archive:
We have written an article on Using a computer to visualise change in
biological organisms showing how the computer software in the MacTutor system can be used to deform pictures in the same way that D'Arcy Thompson used mathematical transformations to alter pictures of biological specimens in On growth and Form . This article includes some of the pictures in On growth and Form .
This article includes another picture of D'Arcy Thompson (with his parrot) taken outside a St Andrews ice-cream shop.
References:
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