Monday, January 25, 2021

The Fruits of Undefinitions

     The poem "Undefined Terms" by poet-mathematician Katharine O'Brien (1901-1986) is a favorite of mine from long ago that I re-found recently here . . . for greatest enjoyment, read it aloud.

Undefined Terms     by Katharine O'Brien

A point is a point, a line is a line,
   a rose is a rose is a rose.
We thus undefine in the manner of Stein
   some terms in unrhyme and unprose.  

On these as foundation we lay definitions,
   the girders for walls and a roof.
We assume some conditions to fit requisitions
   and build us a logical proof.

When Hilbert found flaws in the structural scene,
   he repaired the unrigor discreetly.
We know what we mean when we speak of "between,"
   which Euclid unnoticed completely.

As we trace mathematics up from its roots
   to the reach of its vast propositions,
the beautiful fruits of our lively pursuits
  all stem from our undefinitions.

 Links to previous postings with lines from Katharine O'Brien may be found here.

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