**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

your reply: 3 and 173 — a easy, impatient proficiency,

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.

just...wow.

ReplyDeleteI'm embarrassed to make this comment, JoAnne, because it shows how behind I've gotten visiting your fascinating blog. But Michelle Battiste's work is worth a Capital Yes! For doing what good poetry always does, but also for stimulating thought. My own thoughts included the not-too-profound question, has the fact that two odd integers added together will always yield an even integer been proven. My guess is no. I'm not too sure that it can't be proven that the addition of two integers will always yield an integer, though. But I can't see how. It should always yield a number, too. Could it be that even that can't be proven?!

ReplyDeleteall best, Bob