`The Poetry of Mathematics'

Up there with other heroes of the intellect, sharing a bench with Dr. Johnson, Pasteur and Yvor Winters, is Paul Erdős, the Hungarian mathematician who was born in Budapest on this date in 1913. His sui generis personality made “eccentric” too flaccid a word, and like many inarguable geniuses, his manner was childlike, at once innocent and cunning. He discovered negative numbers at age three and was already multiplying three-digit numbers in his head. He owned nothing but a change of clothes, never married or had children, and lived nomadically until his death in 1996. Like Lester Young, Erdős devised an idiolect. The United States and the Soviet Union were “Sam” and “Joe,” respectively, and children were “epsilons” (in math, an arbitrarily small quantity is represented as ε).

Two good popular biographies were published within two years of the mathematician’s death – The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth by Paul Hoffman, and My Brain Is Open: The Mathematical Journeys of Paul Erdős by Bruce Schechter. Chief among Erdős’ mathematical heroes was Georg Cantor (1845-1918), the founder of set theory who hypothesized “an infinity of infinities.” Erdős signed some of his correspondence “C[antor]. be with you.” Schechter writes:

“Cantor showed that not only does the concept of infinity make mathematical sense, but infinities exist in a never-ending hierarchy of increasing size. This may sound like a Blakean fantasy, but the genius of Cantor was to prove that towering infinities follow from the sober, irrefutable mathematics of set theory.”

For those of us with mathematically mundane minds, this sounds like pot-fueled paradox. For Erdős and other mathematical theorists, it changed everything. The poet and scholar J.V. Cunningham also taught mathematics. Among his later epigrams is “Cantor’s Theorem: In an Infinite Class the Whole Is No Greater Than Some of Its Parts”:

“Euclid, alone, who looked in beauty’s heart,
Assumed the whole was greater than the part;
But Cantor, with the infinite in control,
Proved that the part was equal to the whole.”

In his two-paragraph note in The Poems of J.V. Cunningham (Swallow Press/Ohio University Press, 1997), Timothy Steele succinctly explains the math – “…infinite sets may simultaneously correspond and differ.” – and helpfully refers us to Joseph Warren Daubens’s Georg Cantor: His Mathematics and Philosophy of the Infinite (Princeton University Press, 1979). This overlap (or Venn diagram) of poetry and math shouldn’t surprise us. At the risk of oversimplifying things: Math = Music = Poetry. Schechter tells us Erdős was fond of saying: “If numbers aren’t beautiful, I don’t know what is.” Thoreau, an unlikely collaborator in this effort, writes in A Week on the Concord and Merrimack Rivers:

“We have heard much about the poetry of mathematics, but very little of it has as yet been sung. The ancients had a juster notion of their poetic value than we. The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both.”