[1] Peter Medawar explains this as being because it clearly pioneered the use of mathematics in biology, and helped to defeat mystical ideas of vitalism; but that the book is weakened by Thompson's failure to understand the role of evolution and evolutionary history in shaping living structures.

Philip Ball and Michael Ruse, on the other hand, suspect that while Thompson argued for physical mechanisms, his rejection of natural selection bordered on vitalism.

His most famous work, On Growth and Form was written in Dundee, mostly in 1915, but publication was put off until 1917 because of the delays of wartime and Thompson's many late alterations to the text.

[2] The central theme of the book is that biologists of its author's day overemphasized evolution as the fundamental determinant of the form and structure of living organisms, and underemphasized the roles of physical laws and mechanics.

374 represents precisely the same outline, transferred to a system of oblique co-ordinates whose axes are inclined at an angle of 70°; but this is now (as far as can be seen on the scale of the drawing) a very good figure of an allied fish, assigned to a different genus, under the name of Sternoptyx diaphana.

[13] J. W. Buchanan, reviewing the second edition in Physiological Zoology in 1943, described it as "an imposing extension of his earlier attempt to formulate a geometry of Growth and Form" and "beautifully written", but warned that "the reading will not be easy" and that "A vast store of literature has here been assembled and assimilated".

[14] Edmund Mayer, reviewing the second edition in The Anatomical Record in 1943, noted that the "scope of the book and the general approach to the problems dealt with have remained unchanged, but considerable additions have been made and large parts have been recast".

"[16]The architects Philip Beesley and Sarah Bonnemaison write that Thompson's book at once became a classic "for its exploration of natural geometries in the dynamics of growth and physical processes.

"[18] They note the "extraordinary optimism" in the book, its vision of the world as "a symphony of harmonious forces",[18] and its huge range, including: the laws governing the dimension of organisms and their growth, the statics and dynamics at work in cells and tissues including the phenomena of geometrical packing, membranes under tension, symmetries, and cell division; as well as the engineering and geodesics of skeletons in simple organisms.

[19] He notes that Thompson deliberately avoided invoking natural selection as an explanation, and left history, whether of species or of an individual's life, out of his account.

He quotes Thompson's "A snow-crystal is the same today as when the first snows fell": adding "so, too, the basic forces acting upon organisms",[19] and comments that we have forgotten other early twentieth century scientists who scorned evolution.

)[19]The anthropologist Barry Bogin writes that Thompson's book is a tour de force combining the classical approaches of natural philosophy and geometry with modern biology and mathematics to understand the growth, form, and evolution of plants and animals.

[20]Bogin observes that Thompson originated the use of transformational grids to measure growth in two dimensions, but that without modern computers the method was tedious to apply and was not often used.

[21]The science writer Philip Ball observes that Like Newton's Principia, D’Arcy Thompson's On Growth and Form is a book more often cited than read.

Ball suggests that "The book's central motif is the logarithmic spiral", evidence in Thompson's eyes of the universality of form and the reduction of many phenomena to a few principles of mathematics.

Ruse at once adds that "people like Darwin and Dawkins undoubtedly would disagree";[3] they would insist that the adaptive complexity that we see in the living world simply cannot be explained by physics and chemistry.

[3]For his revised On Growth and Form, Thompson was awarded the Daniel Giraud Elliot Medal from the United States National Academy of Sciences in 1942.

[22] On Growth and Form has inspired thinkers including the biologists Julian Huxley and Conrad Hal Waddington, the mathematician Alan Turing and the anthropologist Claude Lévi-Strauss.

[24] To celebrate the centenary of On Growth and Form numerous events were staged around the world, including New York, Amsterdam, Singapore, London, Edinburgh, St Andrews and in Dundee where the book was written.