The Infinite from Poet’s Pen

“Nature that framed us of four elements,
Warring within our breasts for regiment,
Doth teach us all to have aspiring minds:
Our souls, whose faculties can comprehend
The wondrous architecture of the world:
And measure every wand’ring planet’s course,
Still climbing after knowledge infinite,
And always moving as the restless spheres,
Wills us to wear ourselves and never rest,
Until we reach the ripest fruit of all,
That perfect bliss and sole felicity,
The sweet fruition of an earthly crown.”
(Christopher Marlowe, “Tamburlaine the Great”, 1590)

 “I could be bounded in a nutshell, and count myself a king of infinite space.” (William Shakespeare, “Hamlet”, cca. 1600)

“There’s nothing of so infinite vexation
As man’s own thoughts.”
(John Webster, “The White Devil”, 1612)

“[Infinity is] […] a dark
llimitable ocean, without bound,
Without dimension; where length, breadth, and height,
And time, and place, are lost…”
(John Milton, “Paradise Lost”, 1667)

“As lines (so loves) oblique may well
Themselves in every angle greet:
But ours so truly parallel,
Though infinite, can never meet.”
(Andrew Marvell, “The Definition of Love”, 1681)

“Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in narrowest limits no limit in here.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!”
(Jacques Bernoulli, “Ars Conjectandi”, 1713)

“As lines, so loves oblique, may well
Themselves in every angle greet
But ours, so truly parallel,
Though infinite, can never meet.”
(Andrew Marvell, “The Definition of Love”)

“So, Nat’ralists observe, a Flea
Hath smaller Fleas that on him prey,
And these have smaller Fleas to bite ’em
And so proceed, ad infinitum.”
(Jonathan Swift", “On Poetry: a Rhapsody”, 1733)

“If in the infinite you want to stride,
Just walk in the finite to every side.” (Johann Wolfgang von Goethe)
“To see the world in a grain of sand,
And a heaven in a wild flower;
Hold infinity in the palm of your hand,
And eternity in an hour.”
(William Blake, “Auguries of Innocence”, 1803)

“Action is transitory, - a step, a blow,
The motion of a muscle, this way or that -
’Tis done, and in the after-vacancy
We wonder at ourselves like men betrayed:
Suffering is permanent, obscure and dark,
And shares the nature of infinity.”
(William Wordsworth, “The Borderers”, 1842)

“God puts his finger in the other scale,
And up we bounce, a bubble. Nought is great
Nor small, with God; for none but he can make
The atom imperceptible, and none
But he can make a world; he counts the orbs,
He counts the atoms of the universe,
And makes both equal; both are infinite.”
(Philip James Bailey, “Festus", 1845)

“What miracle of weird transforming
Is this wild work of frost and light,
This glimpse of glory infinite!”
(John Greenleaf Whittier, “The Pageant", 1869)

“Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn have greater fleas to go on;
While these again have greater still, and greater still, and so on.”
(Augustus de Morgan, “A Budget of Paradoxes”, 1915)

“But the star-glistered salver of infinity,
The circle, blind crucible of endless space,
Is sluiced by motion,-subjugated never.”
(Hart Crane. “The Bridge”, 1930)

“Big whorls have little whorls
Which feed on their velocity,
And little whorls have lesser whorls,
And so on to viscosity.”
(Lewis Richardson)

“All finite things reveal infinitude:
The mountain with its singular bright shade
Like the blue shine on freshly frozen snow,
The after-light upon ice-burdened pines;
Odor of basswood on a mountain-slope,
A scent beloved of bees;
Silence of water above a sunken tree :
The pure serene of memory in one man, --
A ripple widening from a single stone
Winding around the waters of the world.”
(Theodore Roethke, “The Far Field” IV, 1964)

Poets and Mathematicians

"[…] it is impossible to be a mathematician without being a poet in soul […] imagination and invention are identical […] the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing." (Sophia Kovalevskaya)

“A mathematician who is not also something of a poet will never be a complete mathematician.” (Karl Weierstrass)

"A mathematician, like a painter or a poet, is a maker of patterns. [...]. The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." (Godfrey Harold Hardy, “A Mathematician's Apology”, 1941)

"The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal." (William James)

“The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.” (Gilbert Keith Chesterton)

"Imagination does not breed insanity. Exactly what does breed insanity is reason. Poets do not go mad […] mathematicians go mad.” (Gilbert Keith Chesterton)

"The imagination in a mathematician who creates makes no less difference than in a poet who invents […]." (Jean Le Rond D'Alembert, Discours Preliminaire de L'Encyclopedie, 1967)

"[…] mathematicians and poets are people who believe in the power of words, of concepts and giving names to concepts" (Cédric Villani)