Sunday, August 27, 2006

The following blog entry is a modified email to a friend at work who keeps my intellect challenged (thank goodness someone does). I figured only about one or two of my readers would even remotely find this interesting, but I figured, "Hey, why the heck not!"

So I did a little research and came up with the following understanding of the Poincaré conjecture, A mathematical conundrum:

Of course, me being curious and all I decided to go on a search and find out more information about the mathematics things you (referring to said friend) were talking about earlier. The problem that was proven was the Poincaré conjecture. Now this concept has been proven for all n dimensions except for 3 (which as it so happens is what most people perceive as our existence dimensions, I'm not in agreement with that, but that's another story). Basically, from what I could gather in simple easy-to-understand terms is that using mathematics you can prove that an object's surface area can be manipulated to look like a sphere's surface area without breaking or cutting that surface area. A torus (or donut shape) for example is not such as object, mostly due to the hole in the center of the shape. A box however could be manipulated to make a sphere surface area. A different way of thinking about this is to draw a loop around any (and every) portion of your object, and if you can move and shrink that loop down to a point on the surface area of your object, then that object is really a three-dimensional sphere. Now all the articles I've read throw around fancy names like manifolds, homeomorphic, and topology, but they would just send me on what seemed to be never-ending dictionary references. I guess the hard thing about this postulate was proving it for three-space. It had already been proven in every other dimension (which is confusing in itself as I have a hard time comprehending a 3 or higher dimensional surface area, but math equations using higher dimensions are much easier to compute than to visualize).

Actually as it turns out, Grigory Perelman, who won the Fields Award (the math noble prize thing you spoke of) for the solution actually declined the nomination and is thinking about perusing other avenues beside mathematics. I think that about sums it all up. Hopefully this is a little easier to understand than what the paper had written in it. Why people are trying to prove something like this just baffles me. Although there is a one million dollar reward for the solution, but Perelman declined that as well.


Andy said...

You and your friend should check out this book The Mobius Strip. The title is a bit longer than that, but I'm not typing it here. It's pretty interesting. Klein Bottles are wacky little buggers. By the way, every math geek should be drinking his beer out of one of these.

Michael said...

WHAT? I have no clue what I just read.