My colleague Michael Thaddeus told me today that James Clerk Maxwell had written a poem on the occasion of the painting of a portrait of Arthur Cayley (by a painter named Dickenson). He was reminded of the poem, which I transcribe below, after reading the quotation in my book from George Salmon’s presentation of Cayley to the general public. I reproduced Salmon’s description of Cayley as part of the historical reconstruction of the theme of the mathematician as artist, but it could also serve to illustrate the topic of my last post on the pure mathematician’s indifference to “material benefit.” The book does not mention that Salmon’s presentation was published in the September 20, 1883 issue of Nature. Here is a photocopy of the relevant passage from the Nature article posted online by the Dolnośląnska Biblioteka Cyfrowa in Wroclaw, Poland:
Elsewhere Salmon writes
One who devotes himself to original mathematical research must make up his mind to forego the pecuniary rewards which attend other forms of literary labour. The public which he addresses is so limited that, instead of expecting to be paid for what he writes, he has to think how he can give it to the world without too severe pecuniary loss. If it were not for the help given by learned societies and by mathematical periodicals, every mathematician who was not rich would be forced to keep his discoveries to himself.
The same issue of Nature ends with a “Plea for Pure Science” abstracted from a speech in Minneapolis by Prof. H. A. Rowland of Baltimore, vice president of Section B (Physics). The “plea” has mostly to do with financial support — “external goods” in the language of my book.
I may return to this plea in a future post; meanwhile, here is Maxwell’s poem:
To the Committee of the Cayley Portrait Fund
O wretched race of men, to space confined!
What honour can ye pay to him, whose mind
To that which lies beyond hath penetrated?
The symbols he hath formed shall sound his praise,
And lead him on through unimagined ways
To conquests new, in worlds not yet created.
First, ye Determinants! in order row
And massive column ranged, before him go,
To form a phalanx for his safe protection.
Ye powers of the nth root of -1!
Around his head in endless circles run,
As unembodied spirits of direction.
And you, ye undevelopable scrolls!
Above the host wave your emblazoned rolls,
Ruled for the record by his bright inventions.
Ye cubic surfaces! by threes and nines
Draw round his camp your seven-and-twenty lines —
The seal of Solomon in three dimensions.
March on, symbolic host! with step sublime,
Up to the flaming bounds of Space and Time!
There pause, until by Dickenson depicted,
In two dimensions, we the form may trace
Of him whose soul, too large for vulgar space,
In n dimensions flourished unrestricted.
I had never previously seen this poem, but I assumed it must have been reproduced fairly frequently; and so it has, including in last year’s book Mathematicians on Creativity, edited by Peter Borwein, Peter Liljedahl, and Helen Zhai, and published by the Mathematical Association of America.
As soon as I saw this book, I checked for the presence of elephants, as I now do in all books about mathematics, and sure enough there are (at least) two, on p. 30 and p. 116. To make sure this was really a peculiarity of mathematics books and not of all books, I checked five books by Jacques Derrida, and found not a single elephant, not even in his book on Husserl’s Origins of Geometry. (All of these searches are done with the help of Amazon’s “Look Inside!” feature.)
The pages of Mathematicians on Creativity just following Maxwell’s poem contain two references to discoveries made in the shower. Checking the index I found that four mathematicians claim to be inspired in the shower. I’m sure this is a nearly universal phenomenon; an explanation would be welcome. Meanwhile, it brings me back to a comment in Chapter 6:
Relatively few professions are practiced even intermittently in the nude, and while Rites is likely to reopen the long overdue debate on whether mathematics… should be one of them…
Rites, of course is the film Rites of Love and Math by Edward Frenkel and Reine Graves. It seems to me that Mathematicians on Creativity settles the issue conclusively.