Chains of Reasoning

     In a recent conversation about mathematics, one of us said, "Mathematics is not about what is true, or cannot be, but is a collection of valid chains of reasoning."  And from there my mind wandered on to Clarence Wylie's sonnet (offered below) -- which is the final poem in a wide-ranging anthology that Sarah Glaz and I edited : Strange Attractors:  Poems of Love and Mathematics (A K Peters/CRC Press, 2008).  Enjoy Wylie's play with thinking about the "holy order" of mathematics.

       Paradox      by Clarence R Wylie, Jr. (1911-1995)

       Not truth, nor certainty. These I forswore
       In my novitiate, as young men called
       To holy orders must abjure the world.  
       “If …, then …,” this only I assert;
       And my successes are but pretty chains
       Linking twin doubts, for it is vain to ask
       If what I postulate be justified
       Or what I prove possess the stamp of fact.

       Yet bridges stand, and men no longer crawl
       In two dimensions. And such triumphs stem
       In no small measure from the power this game,
       Played with the thrice attenuated shades
       Of things, has over their originals.
       How frail the wand, but how profound the spell!