Mr UD was reading through
the 1958 edition of Godel’s
Proof — a book he inherited
from his father — when
this letter fell out of it.
(Click on the pages for
readable images.)
****************
It was from a P. McCleary, in the school of architecture at the University of Pennsylvania, and it was written to Karol’s father, Jerzy Soltan, an architect who taught at Harvard.
The letter wasn’t dated, but its paper was very weathered. Its subject – beauty – is close to UD‘s heart. She’s teaching a course about it this semester at George Washington University.
McCleary sent a book along with the letter, A Mathematician’s Apology, by G.H. Hardy. We easily found this book, with McCleary’s underlinings in it, in our library at home (despite UD‘s math phobia, she has read it). We’re not sure how the letter ended up in Godel’s Proof.
UD quickly discovered that P. McCleary is Peter McCleary, a professor of architecture at Penn, and she wrote to him asking if she could post his letter.
He said sure, and gave me some background on it. He thinks it must have been written “on a bus in the Andes” in the early seventies. He and Jerzy “would discuss his mentor, Le Corbusier, and my mentor (from 1965), Le Ricolais – and often our mentors’ guiding principles. It was probably in that context” that the letter was written.
McCleary’s letter, and Hardy, bring to mind the famous lines from Auden’s poem in memory of Yeats:
poetry makes nothing happen: it survives
In the valley of its making where executives
Would never want to tamper, flows on south
From ranches of isolation and the busy griefs,
Raw towns that we believe and die in; it survives,
A way of happening, a mouth.
Pure, creative, non-utilitarian mathematics, what Hardy calls beautiful mathematics, is like poetry: A discovered pattern, a hidden truth revealed, a new, unexpected, elegant, vivid and vivifying thing. When the pure mathematician discovers something new, the earth says something it didn’t say before: it is given, as Auden says, a mouth.
Architecture (McCleary cites Palladio and Alberti) is that peculiar art that sometimes combines Hardy’s abstract aesthetics with the grounded, practical, embodied world.
UD‘s grateful to McCleary for taking out his pen on the bus in the Andes. She’s grateful for a number of reasons, but this is perhaps the strongest: He returned her to this remarkable bit of prose from Hardy. Hardy wrote A Mathematician’s Apology toward the end of his life, and in this passage he reflects on his existence:
I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, ‘Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.’ It is to them I owe an unusually late maturity: I was at my best at a little past forty, when I was a professor at Oxford. Since then I have suffered from that steady deterioration which is the common fate of elderly men and particularly of elderly mathematicians. A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.
It is plain now that my life, for what it is worth, is finished, and that nothing I can do can perceptibly increase or diminish its value. It is very difficult to be dispassionate, but I count it a ‘success’. I have had more reward and not less than was due to a man of my particular grade of ability…
My choice was right, then, if what I wanted was a reasonably comfortable and happy life. But solicitors and stockbrokers and bookmakers often lead comfortable and happy lives, and it is very difficult to see how the world is the richer for their existence. Is there any sense in which I can claim that my life has been less futile than theirs? It seems to me again that there is only one possible answer: yes, perhaps, but, if so, for one reason only.
I have never done anything ‘useful.’ No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world. I have helped to train other mathematicians, but mathematicians of the same kind as myself, and their work has been, so far at any rate as I have helped them to it, as useless as my own. Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.
The case for my life, then, or for that of anyone else who has been a mathematician in the same sense in which I have been one, is this: that I have added something to knowledge, and helped others to add more; and that these somethings have a value which differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any of the other artists, great or small, who have left some kind of memorial behind them.
***************************
I’ve put McCleary’s letter back inside the pages of Hardy’s Apology, where it belongs.
***************************
UPDATE: Maurice, a reader, emails UD:
“Little did Hardy suspect that his branch of mathematics (Number Theory) would become the basis for security on the Internet.”
UD loves ironies like this.
Maurice links her to this page.
[T]oday’s Internet commerce makes heavy use of encryption techniques that depend upon results in number theory, a branch of mathematics that until relatively recently was thought of as strictly “pure mathematics,” with no real-world applications. In his book A Mathematician’s Apology, the famous British number theorist G. H. Hardy declared “The ‘real’ mathematics of the ‘real’ mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Riemann, is almost wholly ‘useless’.” Yet it is mathematics developed by those very mathematicians, along with Hardy himself, that keeps today’s Internet transactions secure.
