“Of the chemistry of his day and generation, Kant declared that it was a science, but not Science - eine Wissenschaft, aber nicht Wissenschaft - for that the criterion of true science lay in it’s relation to mathematics.  This was an old story: for Roger Bacon had called mathematics porta et clavis scientiarum, and Leonardo da Vinci had said much the same.  Once again, a hundred years after Kant, Du Bois-Reymond, profound student of the many sciences on which physiology is based, recalled the old saying, and declared that chemistry would only reach the rank of science, in the high and strict sense, when it should be found possible to explain chemical reactions in the light of their causal relations to the velocities, tensions and conditions of equilibrium of the constituent molecules; that, in short, the chemistry of the future must deal with molecular mechanics by the methods and in the strict language of mathematics, as the astronomy of Newton and Laplace dealt with the stars in their courses.  We know how great a step was made towards this distant goal as Kant described it, when van’t Hoff laid the firm foundations of a mathematical chemistry, and earned his proud epitaph - Physicam chemiae adiunxit.

    ...We need not wait for the full realisation of Kant’s desire, to apply to the natural sciences the principle which he laid down.  Though chemistry fall short of its ultimate goal in mathematical mechanics, nevertheless physiology is vastly strengthened and enlarged by making use of the chemistry, and of the physics, of the age.  Little by little it draws nearer to our conception of a true science with each branch of physical science which it brings into relation with itself: with every physical law and mathematical theorem which it learns to take into its employ.  Between the physiology of Haller, fine as it was, and that of Liebig, Helmholtz, Ludwig, Claude Bernard, there was all the difference in the world.

    As soon as we adventure on the paths of the physicist, we learn to weigh and to measure, to deal with time and space and mass and their related concepts, and to find more and more our knowledge expressed and our needs satisfied through the concept of number, as in the dreams and visions of Plato and Pythagoras; for modern chemistry would have gladdened the hearts of those great philosophic dreamers.  Dreams apart, numerical precision is the very soul of science, and its attainment affords the best, perhaps the only criterion of the truth of theories and correctness of experiments.  So said Sir John Herschel, a hundred years ago; and Kant had said that it was Nature herself, and not the mathematician, who brings mathematics into natural philosophy.

    But the zoologist or morphologist has been slow, where the physiologist has long been eager, to invoke the aid of the physical or mathematical sciences; and the reasons for this difference lie deep, and are partly rooted in old tradition and partly in the diverse minds and temperaments of men.  To treat the living body as a mechanism was repugnant, and seemed even ludicrous, to Pascal; and Goethe, lover of nature as he was, ruled mathematics out of place in natural history.  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 physical, 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.  In short, he is deeply reluctant to compare the living with the dead, or to explain by geometry or by mechanics the things which have their part in the mystery of life.  Moreover he is little inclined to feel the need of such explanations, or of such extension of his field of thought...”

D’arcy Thompson - On Growth and Form (Introductory)