Monday, April 12, 2010

Poetry and Mathematics -- Similarities

HOW are mathematics and poetry similar?

Often-quoted in mathematical circles are words from mathematician Karl Weierstrass (1815-97): “It is true that a mathematician, who is not somewhat of a poet, will never be a perfect mathematician.”    And from physicist Albert Einstein (1879-1955):  "Pure mathematics is, in its way, the poetry of logical ideas." More recently, from Lipman Bers (1914-1993): “  . . . mathematics is very much like poetry . . . what makes a good poem—a great poem—is that there is a large amount of thought expressed in very few words."

I agree with each of these quotations, but they overlook another key similarity between mathematics and poetry--the appreciative awe experienced by mathematicians and poets when they encounter great work.  An occasional mathematical proof--for example, an elegant rendering of Euclid's proof of the infinitude of the primes--takes my breath away with the depth, power and beauty of the ideas; that is, the proof affects me with the same gasp of delighted amazement as does a very special poem (such as Richard Wilbur's "Love Calls Us to the Things of This World").

To explore math-poetry comparisons, the following "fill-in-the-blank" statements can be useful.  Some of these statements have been made by poets and some by mathematicians--and either "poetry" or "mathematics" (or a slight variant such as "poem" or "mathematician") correctly fills each blank.  While pondering choices for the missing words, similarities between mathematics and poetry come into view.

(1)  ______ is the art of uniting pleasure with truth.
(2)  To think the thinkable -- that is the ______'s aim. 
(3)  All ______ [is] putting the infinite within the finite.
(4)  The moving power of ______ invention is not reasoning but imagination.
(5)  When you read and understand ______, comprehending its reach and formal meanings, then you master chaos a little.
(6)  ______ practice absolute freedom.  
(7)  I think that one possible definition of our modern culture is that it is one in which nine‑tenths of our intellectuals can't read any ______. 
(8)  Do not imagine that ______ is hard and crabbed, and repulsive to common sense.  It is merely the etherealization of common sense.        
(9)  The merit of ______, in its wildest forms, still consists in its truth; truth conveyed to the understanding, not directly by words, but circuitously by means of imaginative associations, which serve as conductors.    
(10) It is a safe rule to apply that, when a ______ or philosophical author writes with a misty profundity, he is talking nonsense.    
(11) ______ is a habit.      
(12) . . . in ______ you don't understand things, you just get used to them.   
(13) ______ are all who love--who feel great truths
       And tell them.  
(14) The ______ is perfect only in so far as he is a perfect human being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, comprehensive, pure, clear, attractive, and even elegant.   
(15) . . . [In these days]  the function of ______ as a game . . . [looms] larger than its function as a search for truth . . . .   
(16) A thorough advocate in a just cause, a penetrating ______ facing the starry heavens, both alike bear the semblance of divinity.   
(17) ______ is getting something right in language.

The words missing are(1) Poetry  (Samuel Johnson), (2) mathematician (Cassius J. Keyser), (3) poetry (Robert Browning), (4) mathematical (Augustus De Morgan), (5) a poem (Stephen Spender), (6) Mathematicians (Henry Adams), (7) poetry (Randall Jarrell), (8) mathematics (Lord Kelvin), (9) poetry (T.B. Macaulay), (10) mathematician (A.N. Whitehead), (11) Poetry (C. Day-Lewis), (12) mathematics (John von Neumann), (13) Poets (P.J. Bailey) , (14) mathematician (Johann Wolfgang von Goethe), (15) poetry (C. Day‑Lewis), (16) mathematician (Johann Wolfgang von Goethe), (17) Poetry (Howard Nemerov).  

This posting borrows from an old publication of mine in the American Mathematical Monthly, Vol. 99, No. 2 (February 1992).  It also was part of "Mathematics and Poetry: Isolated or Integrated," Humanistic Mathematics Network Newsletter #6 (May 1991).


  1. The beauty of poetry and mathematics lies in their compression. Shakespeare says that "Brevity is the soul of wit [intelligence]", and Ockham's razor maintains that the most economical explanation is the most persuasive. Poetry reminds me of nuclear fusion: small amounts of matter cause incredibly large explosions.

  2. It seems that one could put philosophy in the blanks as well or even most branches of philosophy.