Saturday, January 26, 2013

Poetry at JMM -- groups, etc.

     A math-poetry reading on January 11 at the Joint Mathematics Meetings in San Diego -- organized by Gizem Karaali (an editor of the Journal of Humanistic Mathematics) and Sue VanHattum (blogger at Math Mama Writes) -- has been featured in Evelyn Lamb's Scientific American blog.  

Next year's JMM will be in Baltimore, MD during January 15-18, 2014.  
There will be a poetry reading -- details will be posted here when they're available.

     Sandra DeLozier Coleman is a retired mathematics professor who has for many years written poems that relate to math.  Her poem (presented below) about the definition of a mathematical group was featured in the Scientific American blog.  When DeLozier read the poem in San Diego, her introduction to it included these words: "I’m poking a bit of fun at the futility of expecting a mathematician to explain a math concept, as familiar to him as his name, in language even a first week student will understand. Here the voice is of an Abstract Algebra professor who is attempting to explain what makes a set a group in rigorous rhyme!" 
     Coleman's comment and her poem illustrate one of the ongoing dilemmas for mathematicians.  How to be poetic and also to inlcude the careful detail that mathematics requires.  Many poems that delight non-mathematicians give a shudder to a mathematician because mathematical terms have been used with "poetic license" rather than with precision. 
     Many items of mathematics are poetry -- elegant principles, theorems, and proofs that offer a mathematician that repeatable whole-self reaction that comes from a fine poem.  But it is very difficult to translate mathematics into English and preserve mathematical beauty.  (Here, for example, is a link to a proof proposed as a poem.)

Group: n. collection, cluster, set, assembly     
                                                           by Sandra DeLozier Coleman

“Define a group,” the student asks.
(I hope I’m equal to the task
of showing that by “group” is meant
more than a set of elements.)

We’ll need a set that’s well-defined,
where pairs of elements combined
are members of the set as well.
(He’s with me, so far, I can tell.)

The rule for forming combinations
Must hold for all associations,
Although commutativity
Is not a real necessity.

Except for the identity.
(But that’s a special case you see!)
Indeed, this member of the set
Is that peculiar element,
Which paired with any other there
Returns the other of the pair.
What’s more each member of the set
Must have a partner element,
Which pair combined must always be
This very same identity.

The student looks a little dazed.
Now, is he lost or just amazed?


A note to the non-mathematical reader:  Often a "mathematical group" is introduced as a partnership between a set and an operation; that partnership must have four properties -- outlined in Coleman's poem and typically known by these names: Closure, Associativity, Identity and Inverses.  (For example, the integers partnered with addition form a group; the integers partnered with subtraction do not form a group.)
     Coleman has, in addition to her own poetry, an ongoing project of translating into English poetry and other writing by the very fine Russian mathematician Sophia Kovalevsky (1850-1891).

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