January 15, 2013 | 5
I am home from the Joint Mathematics Meetings, and I’m still trying to process everything I learned and got fired up about there. Most of my time was spent in formal, serious lectures, many of them quite technical, but on Friday night, I went to something completely different: a mathematical poetry reading, facilitated by the Journal of Humanistic Mathematics. Some of the featured poets are mathematicians or math teachers, while some are full-time writers with an interest in math.
Mathematics is often portrayed as a sterile, robotic discipline, but many mathematicians find it to be an emotional, human endeavor. The mathematical poetry session tapped into those emotions in very direct ways, but I also feel it when talking with researchers in my field of study or struggling with a math problem that won’t quite work the way I want it to.
My favorite poem of the night was “Group: n. collection, set, assembly,” by Sandra DeLozier Coleman, who has graciously allowed me to share it below. The poem is more than a poem: it is also an accurate definition of a mathematical group. (As is often the case, mathematics uses a standard English word in a very precise way.)
To me, this poem captures the gap that sometimes exists between student and teacher, and I can see myself in both roles. If you’re curious about the mathematical underpinnings of the poem, try Wolfram MathWorld’s Group page. I’m interested in other creative expressions of the mathematical concept of group. If you know of any, please share them with me in the comments or on Twitter. And for more mathematical poetry, check out the M@h(p0et)?ica series on the Guest Blog.
Without further ado, here is the poem, along with Sandra DeLozier Coleman’s introduction.
In this second poem 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!
Group: n. collection, cluster, set, assembly
“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,
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?