D’Arcy Thompson’s celebrated book On Growth and Form was published 100 years ago.
To celebrate this and the fact that Thompson was Professor of Mathematics at St Andrews for 64 years (and had been at Dundee before that, for part of which time it was a campus of St Andrews), the University had a small meeting, culminating in a public lecture by Evelyn Fox Keller, which I attended.
Thompson was clear in his belief that the laws of biology did not contain any new principles beyond the laws of physics and mathematics. He was keen to explain biological development on the basis of mathematical laws. He also looked very carefully at things, a skill which perhaps some mathematical biologists don’t have to the same degree.
That is all I learned about Thompson from Keller’s lecture, which was more about the history of biology in the twentieth century. Thompson had the misfortune to be writing just as genetics was getting into its stride, and it seems that for a good part of the twentieth century, people believed that “the gene” was a biological principle, analogous to the atom (or the elementary particle) in physics, but not itself reducible to mathematics and physics. So Thompson’s work, at a stroke, became unfashionable. He wrote in On Growth and Form: “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.”
I would naively have thought that the eludication of the structure of DNA strengthened Thompson’s position, since the geometry of the molecule and its interactions with things such as methyl radicals seem to be amenable to study by mathematics and physics, and we know now that these play an important part in the action of genes.
But I am afraid to say that the lecture did reinforce my belief that, on the whole, historians read papers whereas mathematicians put on a performance; moreover, the lecturer seemed to be unaware that she was giving a public lecture rather than just the closing lecture of a specialist conference, and she really was unaware that the printed text that she was reading omitted lines here and there.
Still, she can give me eleven years, so I suppose I should simply hope that I am still in the business when I reach her age.
You can read more about D’Arcy Thompson here, on the St Andrews History of Mathematics website.