The Mesmerism of Mathematics
A 19th-century love letter to the most limitless medium of thought.
By Maria Popova
Mathematics is at once the most precise and the most abstract instrument of thought — a convergence of symbol and sentience utterly poetic in its ability to convey the most complex underlying laws of the universe in stunning simplicity of expression. It mirrors the world back to itself both condensed and expanded, granting us an enlarged understanding through the art of distillation. Ada Lovelace considered mathematics the “poetical science” and, in contemplating the nature of the imagination, called it “the language of the unseen relations between things.” Perhaps E = mc2 is the greatest line of poetry ever written, then. At the very least, it inhabits the same world as “To be, or not to be”; it is the mathematical counterpart to “the still point of the turning world.” So is it any wonder that mathematics renders some of humanity’s most potent minds nothing short of besotted?
Hardly anyone has captured the mesmerism of mathematics more beautifully than the pioneering 19th-century English mathematician James Joseph Sylvester (September 3, 1814–March 15, 1897) in a magnificent speech he delivered on February 22, 1877 in Baltimore.
I often say that literature is the original internet: A footnote — that ancient analog hyperlink — in Oliver Sacks’s masterwork of science and spirit, Awakenings, led me to Sylvester’s speech, included in The Collected Mathematical Papers of James Joseph Sylvester: Volume III (public library) under the title “Address on Commemoration Day at Johns Hopkins University.”
Sylvester considers this difficult art of conceptual condensation:
It is the constant aim of the mathematician to reduce all his expressions to the lowest terms, to retrench every superfluous word and phrase, and to condense the Maximum of meaning into the Minimum of language.
And yet the joy of mathematics, he argues, isn’t an esoteric pursuit reserved for academically trained mathematicians — rather, it is a supreme and universal delight of the human mind at play with itself:
I have reason to think that the taste for mathematical science, even in its most abstract form, is much more widely diffused than is generally supposed…
This wide appeal of the mathematical spirit, Sylvester observes, stems from its immensity of scope and its infinite range of intimacies with the nature of the world:
Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer’s gaze: it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness, the life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud and cell, and is forever ready to burst forth into new forms of vegetable and animal existence.
Every science becomes more perfect, approaches more closely to its own ideal, in proportion as it imitates or imbibes the mathematical form and spirit.
Complement with the illustrated story of legendary mathematician Paul Erdős and mathematical genius John Horton Conway on the art of being a professional nonunderstander.
Published February 22, 2016