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D'Arcy Thompson senior was appointed Professor of Greek at Queen's College (now University College) Galway when D'Arcy was 3 years old. D'Arcy lived part of the time with his grandfather Joseph Gamgee and from the age of ten he attended Edinburgh Academy. There he won the prize for Classics, Greek Testament, Mathematics and Modern Languages in his final year at school. He recalled in a letter to the Times that :

... in his class at Edinburgh Academy was one boy who won the Victoria Cross, one with a seat in the Cabinet, one Royal Academician, and four Fellows of the Royal Society .

After starting a medicine course at Edinburgh University in 1877 he studied this for three years before he changed to study zoology at Trinity College, Cambridge.

In 1880 Thompson was a sizar, meaning that he obtained financial support by acting as a servant to the older boys, then in 1881 he was awarded a scholarship. There was a group of young Cambridge men who were lying the foundations of the science of biology at this time and Thompson quickly became part of the group. He took the Natural Sciences Tripos and graduated with a B.A. in Zoology in 1883. After graduating he spent one further year at Cambridge acting as a demonstrator on physiology.

In 1884 D'Arcy Thompson was appointed Professor of Biology in Dundee (incorporated as part of the University of St Andrews in 1897) and later the title of his chair was changed to natural history. He set to work building up a zoology museum in Dundee to be used both for teaching and research. He collected a wide range of specimens from the Arctic waters making voyages himself as a commissioner for a joint British-American inquiry into fishing for seal fur in the Bering Sea. In his role as commissioner he visited the Pribylov Islands in the Bering Sea in 1896 and 1897, being honoured with being made Commander of the Bath in the following year for the services he had given. Also in 1898 he was appointed to the Fishery Board for Scotland. He was a British representative on the International Council for the Exploration of the Sea from the time it was set up in 1902. While he was professor in Dundee, Thompson married Ada Maureen Drury in 1901. They had three daughters.

While at Dundee he showed another side to his character when he became a founder member of the Dundee Social Union. He pressed for it to buy four slum properties in the town which they renovated so that the poorest families of Dundee could live there.

In 1917 D'Arcy Thompson 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. The breadth of his learning is emphasised in :

Thompson did not fit into any particular category: he was equally a scholar, scientist, naturalist, classicist, mathematician, and philosopher. Inheriting a love of the classics from his father and brought up by his scientific grandfather, he straddled two worlds and dominated both.

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. On Growth and Form:

... departed from contemporary zoology, which was occupied with orthodox questions of comparative anatomy and evolution, and treated morphological problems by mathematics. the theme was original, unorthodox, and revolutionary.

Let us quote D'Arcy Thompson's own view from the introductory chapter of his masterpiece:

It behoves us always to remember that in physics it has taken great men to discover simple things. They are very great names indeed which we couple with the explanation of the path of a stone, the droop of a chain, the tints of a bubble, the shadows in a cup. It is but the slightest adumbration of a dynamical morphology that we can hope to have until the physicist and the mathematician shall have made these problems of ours their own.

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 . He was critical of other zoologista for not taking a mathematical approach:

Even now the zoologist has scarce begun to dream of defining in mathematical language even the simplest organic forms. When he meets with a simple geometrical construction, for instance in the honeycomb, he would fain refer it to psychical instinct, or to skill and ingenuity, rather than to the operation of physical forces or mathematical laws; when he sees in snail, or nautilus, or tiny foraminiferal or radiolarian shell a close approach to sphere or spiral, he is prone of old habit to believe that after all it is something more than a spiral or a sphere, and that in this 'something more' there lies what neither mathematics nor physics can explain.

See this link for a much fuller quote from the introduction to D'Arcy Thompson's On Growth and Form (1917) which explains his views on mathematics and biology.

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.

His deep knowledge of the classics was not just a hobby, for he published many papers on the topic. His most important publications in this area were A glossary of Greek birds (1895), a translation of Aristotle 's Historia Animalium (1910), and A glossary of Greek fishes (1945). In fact fishes were of great interest to Thompson who was highly involved with the international organisation and regulation of fisheries as we mentioned above.

Another of his interests was in the history of St Andrews, and he was a founder member of the St Andrews Preservation Trust. He would say:

The stones cry out to us as we pass and tell us the story of our land.

His book Science and the classics discusses "improvements" to the town which he considered destroyed its beauty.

D'Arcy Thompson was elected a Fellow of the Royal Society of London in 1916 and was vice-president of the Society in 1931-33. He was awarded the Darwin Medal of the Society in 1946:

... in recognition of his outstanding contributions to the development of biology.

He also received recognition for his mathematics, being made an honorary member of the Edinburgh Mathematical Society in 1933. He was President of the Classical Association in 1929 and President of the Royal Society of Edinburgh in 1934-39. He received the Linnean Gold Medal from the Linnean Society in 1938. He was knighted in 1937.

W T Calman, writing in the Dictionary of National Biography, says that D'Arcy Thompson:

... was a man of very distinguished presence, a ready and polished speaker, whose lectures and addresses displayed a range of interests and of knowledge that would have been remarkable at any time but seemed doubly so in our age of specialists. He loved teaching and taught to the very last, for even in his final illness he gathered his honours students in his sick room for talks that none of them will forget.

It is also noted in that he was:

... an ardent correspondent both to individuals and newspapers and many penetrating and sensible letters of his appeared in the Times. With all his intellectual distinction he will be remembered by his friends, old and young, as an outstanding figure and a charming character.

Source:School of Mathematics and Statistics University of St Andrews, Scotland