When is a coffe mug the same as a bagel?

The recent citation in the New York Times (further quoted by Steven Colbert in the Cobert Report) about a mathematical proof brought back to me dear memories of what now seems like a prior life.

Grigory Perelman, a Russian mathematician from St. Petersburg has proved what is known in the math world as Poincare’s Conjecture. This isn’t a recent development. He posted a preprint of his proof in 2002 and filled in many of the details during a speaking tour in 2004. It was only this year, however, when the possibility arose of his receiving the prestigious Fields Medal for mathematical excellence and/or a $1 million prize from the Clay Mathematics Institute that the proof suddenly became newsworthy. Some news media were even using phrases like “this could change the way we view our universe”. Poppycock! Everyone has assumed Poincare’s Conjecture was true since he proposed it in 1900 but the proof has been elusive. Now that it’s proven, mathematicians can go onto other things but our view of the universe isn’t going to change because of it.

I have a Masters degree in mathematics. When I was actively studying it, this branch of math, called topology, was probably my favorite. Topologists look at the world in a strange, highly symbolic way with objects in 2, 3, 4 and higher dimensions defined by their unchangeable properties. Spheres don’t have to be round like in geometry or algebra. They just have to be closed and have no “holes” in them. Thus a block, a ball, or an elephant shaped soap bubble (remember Dumbo?) can be molded into a 3-sphere (a sphere in 3 dimensional space). But a donut, a bagel, or a coffee cup can’t be. Topologists love to “deform” objects, remold them like clay models, to tease out which properties are unchangeable and which aren’t.

In topology we would prove, as well as dream up, theorems and conjectures. These are the ideas that filled my head while mindlessly cleaning acres of floors for the telephone company or drifting off to sleep at night. More than once, Carolyn was rudely awakened as I would suddenly sit up in bed with an “Aha!” moment and grab a pencil by the side of the bed to jot a potential proof down before it escaped my thoughts. Amazing how good the good old days can look when you’re looking back 40 years.