> "No mathematician can be a complete mathematician unless he is
> also something of a poet."
What I find deeply disturbing is that there is more an interest
in the source than the sense. And not the sense of what the utterer had
in mind -- but what its most profound sense could be (and whether it has
a worthwhile sense; without this sort of consideration, one does not
have substantial history, but only toy history). I've seen variations
on that quote used in the wholly wicked sense of being thrown out with a
profound air by way of supposedly reassuring students or general
scientific public that math. is not cold abstraction or boring
calculation, but shares in "poetry" [the sort of pathetic unifying of
the two cultures one finds in say Kline, e.g., a little linear
perspective, a little projective geometry and one is supposed to be
impressed that the two cultures and not so separate after all). This
really leaves no one the wiser, such a quote as this. There is of
course a huge literature that tries to claim that mathematics is like
poetry in that a creative mathematician will rely on metaphor, or more
generally trope, just like the poet. This itself is two ways silly and
superficial -- we all use trope all the time. Indeed, there are
excellent critics/poets who will insist that "literalness" is itself a
trope. It has been remarked saliently by the Renaissance master of
poetic, Abraham Fraunce, that any poem which (excepts as a joke or a
lampoon) contains a stand-out metaphor is a failed poem, or the reader
has failed to read the poem well (as critics and even more to the point
linguists are very bad readers of poetry!).
There is a kind of connection of analogy between poetry and
mathematics -- in developing mathematical ideas and concepts, it is
finally our logical sense and criticism or tacit or explicit logical
form that dictates the possible final shapes of the concepts or ideas
undergoing mathematicization -- this invariably introduces whole rafts
of subtleties and distinctions and novel conception that were not in the
original conceptions/ideas themselves. Poetry, the real stuff, not
the coffee house slam verse, works within a more fluid, but perhaps
equally rigid possibilities of form (in analogy with logical form),
which varies with languages. Say for example English blank verse (to
take a moderately free form) -- one still has to count syllables,
etc etc., and there has to be a kind of meshing or coherence of sense
which poets themselves call "logical" (except of course where the poet
has set out to make fun of logic, but even that fun-making with have a
coherence to it worthy of being called "logical"). (For English
speakers, worth seeing John Hollander's RHYME'S REASON; also see
Rosemond Tuve's writings on Renaissance poetic and logic)
Here is the point -- that ordinary language will rarely fit into
any of these formal requirements. One can't have an idea which one then
just expresses in a poem. rather the act of composing a poem will
necessary transform/deform/enrich/refine language, "turn it" (hence --
"trope"), opening up altogether hitherto unexpressed and unthinkable
thoughts. This in outline is a perfect match with the way creative
mathematics works -- pressing as yet only premathematical or
incompletely mathematical ideas into logical form opens up sometimes
dizzying and maddening fields of novel distinctions, questions,
conceptions, new combinations that could not have been engendered and
valued without that press toward logical rigour. The point Plato missed
-- one gets new ideas, new vistas by pressing something into a form
that is not native to it. That's the creative principle in poetry and
mathematics.
robert tragesser
west(running)brook, connecticut