## Wednesday, September 22, 2010

### Goldbach's conjecture -- easily stated but unsolved

This blog's July 20 posting featured work from poets who have spouses or siblings who are mathematicians.  Today, introducing the work of  Michele Battiste (who considers Goldbach's conjecture), we again honor that theme.  Goldbach's conjecture asserts that every even integer greater than 2 can be expressed as a sum of two prime integers.   For example, 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 7 + 3 or 5 + 5, and so on.  The conjecture was first proposed in 1742 by German mathematican Christian Goldbach in a letter to Swiss mathematician Leonhard Euler -- and in 2010--though it has been verified for many, many, many even integers--it still remains unproved.

Postulates impossible to prove are the easiest ones to grasp,
an application of Golbach’s Conjecture:       by Michele Battiste

every even number
greater than 2 can be expressed as the sum of two primes,
which makes a great game on the uptown A-train from West 4th
Street to 101st – a competition of elegance with empty pockets.
Example: 88 = 17 + 71, symmetry trumping the easy 83 + 5,
the clumsy 29 + 59, the claim that 41 + 47 works
just as well.
But examples are entitled to nothing. Somewhere between Times
Square and 59th he says stop being pretty. Prove it’s true.

Truth is, we blew our 40 bucks on 4 drinks at Zinc Bar.
Job offers and tomorrow’s lunch are ghosts we hope are real.
The money will come from somewhere. Hypothesis guards
its logic with good reason.

Attempts at proof: the properties of magnetism,
the bounty of primes, the indiscretion
of addition – an affair of 4 months = a cross-continental
move

Never mind that our great Thai restaurant find
turns out to be a chain, or tonight’s accommodation is a twin
bed and a shared toilet down the hall, this city has
an ocean and somewhere an empty room waits
for us to come and undress and be quiet, settle in
each other.

Somewhere near 96th Street I give up equations,
lay my head on his chest and count the clicks
by ones. He gives me a solution.

“No one has yet proven it, and nobody
has proven it wrong.”

"Postulates . . . ." (above) first appeared in Mid-American Review (2007/8) and "Splitting . . ." (below) first appeared in Pool  (2007). Poet Michele Battiste is married to a mathematician whose job title is software engineer, She got partway into calculus in high school and met truth tables in college. Her favorite algebraic postulate is the Transitive Property of Equality -- "it's so inclusive."

Splitting the Distance, an advanced application
of Goldbach's Conjecture:     by Michele Battiste

every number greater
than 3 can be expressed as the average of two primes or
as this: You don't know how to dress
for a New York winter; in Wichita,
my parka grows musty from neglect.
or this: The graphite in your freshly purchased
mechanical pencil is a compromise, stiff
enough to ache a little, soft enough
not to break.

These plains are yours, this postulate, this pad of graph paper you
left behind. My voice echoes through the phone, offering 88.
Manhattan leans heavy, the air thick with signals in
but without me you got your head caught in the subway doors.
The crowded car stared at the amazing lack of symmetry.

Wichita is dry tonight, shriveling. The west-bound
wind could snatch the napkin from your lap
as you sit in Washington Square eating dosas, but it lost
your greasy thumbprint in Brazil, Indiana. That city is like every
city — filled with mathematicians without solutions. This city
has a ghost town woman lost in contemplation of

the Given: a finite set of integers that never fail
the gap from there to here.
I wanted 79 and 97, split like twins and pressed together. I want
to hollow out the number line and throw digits in the river.