I’m reading G.H. Hardy’s A Mathematician’s Apology, an elegant essay written towards the end of Hardy’s long and illustrious career in pure mathematics. I’m enjoying it very much. It allows me some insight (I hope) into the mind and work of my son, Brendan, who works in the field of optimal transportation as well as mathematical economics and physics.
This essay begins with a statement that locates its writer in age rather than youth. “It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.” There are of course parallels with many other areas of human investigation and creative practice. Young writers write, don’t they? They tend not to think too much about exposition or justification. Painters, too. They plunge into the work they are called to do and it’s only later, in retropect, that they attempt to figure out the patterns of this work, its context (if it’s lucky enough to have one — or many…), the connections between their work and that of their peers or predecessors.
But I’m thinking how lucky I am to have found this book which gives me some insights in the workings of an intelligence so mysterious to me. I’ve read about half of it and have some questions: all those theorems that I’m coming to, so beautiful in their abstract language, like Greek; when I look at a page of Greek, I can make out perhaps 1/8 of it but I know that using my lexicon, I can probably figure out more. Will this be the case with Euclid’s proof of the existence of an infinity of prime numbers? We’ll see.
There is much that I admire in this essay, even if I don’t necessarily agree with statements like this one: “A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.” I think of William Carlos Williams here and his poetic philosophy of intent:
— Say it, no ideas but in things —
nothing but the blank faces of the houses
and cylindrical trees
bent, forked by preconception and accident —
split, furrowed, creased, mottled, stained —
secret — into the body of the light! (from Paterson)
Maybe we are all closer than we think we are, closer in our searching for meaning in those blank faces of houses, the cryptic notion of an infinity of prime numbers, and the beautiful patterns of the world that inspire one person to make equations and another to make poems or vast canvasses filled with angels or to translate one to another so that I can sit with a notebook, wondering how to work this illustration of Mendel’s law into both an essay on family history and a quilt.
Dominant and recessive phenotypes. (1) Parental generation. (2) F1 generation. (3) F2 generation.