(an excerpt from the novel, Human History of Mathematics)
There is no straight line without depth, and there are no perfect circumferences. The imagination that Euclid requires—since the third century before Christ to today—of whoever reads his Elements is bigger than the one necessary to follow the stories of gods and heroes.
The friezes of the Greek temples could have told of parallels, triangles, and figures whose existence coincide and end with the grandiose description Euclid made of them, just as the sirens and the Hippocentaurs exit only in mythology, or in dreams. However, though someone may have sworn to have seen a Hippocentaur—and it was not so big, Phlegon assures us—or to have been tied to the mast of a ship to hear, without dying, the siren song, no one has ever intersected a point without dimension, nor did he ever boast of having seen it.
Euclid’s reasoning, theorems, constructions, and demonstrations apply only to these non-existent forms, and every time that I have drawn a triangle from that world of perfection, or drawn a segment, what I have done—I, like everyone—was to imagine. Imagine with exactness and concentration, without mingling men with horses, women with fish. An imagination that does not transform, but creates. Which is not metamorphosis, but invention. Before learning geometry—I, like everyone—imagined that my point marked with a pin had no dimension; that is, to have in front of me what I needed, or what I desired. To prove the Pythagorean theorem, more imagination is needed than to bring the dead back to life, because those, at least once, have been there. But the lines, the points, the geometric figures—never. Therefore, all that Euclid speaks of, does not exist. In no verbal time.
On the other hand, the points, alone or aligned to form lines or planes, are the elements of the only grammar that, in addition to describing and communicating the world, was able to build and manage devices that have sent us beyond the fixed stars, and further.
Mathematics (and I think of it every time I find myself in front of a drawing on a wall, on a bridge or on the asphalt of any city), is this imagination that educates the invisible—and therefore to love—the dead, utopias and ghosts, and that has taken us far away, in time and space. It is this exercise of imagination that makes us, and allows us to remain human, and therefore, after all, it matters little that everything that Euclid speaks does not exist, if we are here.
—Translated by Malina Mannarino
Chiara Valerio received a doctorate in Applied Mathematics and is active as a writer, journalist, essayist and translator. She is the editor of Nuovi Argomenti; the Italian fiction editor at Marsilio Publishers; a curator of cultural programs for public radio; and a regular contributor for various newspapers and magazines. Her writing draws on the rich history of scientific thought to address the IT revolution and globalization. She has written novels and short stories, including Almanacco del giorno prima (2014), Storia umana della matematica (2016), and is the Italian translator of Virginia Woolf’s Flush, and Freshwater.