The Beauty of Math

So...

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One of my students today had the audacity to say my blog wasn't really a blog because I don't really blog, I just assign! Okay, so here's a blog!

One of the things I find absolutely engaging about math is its inherent beauty. There are aspects of the study of math that draw any thinking person to ask profound questions. The essence of learning and the acquisition of knowledge begins simply with a wonder about something...and I cannot think of anything else that makes me wonder why more often than do mathematically inspired questions. One of the earliest questions I remember that caused me to take pause was a question about the circle.

Something seemingly as dry as the study of irrational numbers becomes something more when you consider a question like... Why is the ratio of a circle's circumference to its diameter always a number that cannot ever be expressed as the ratio of two integers? Why does pi appear in many formulas seemingly unrelated to a circle? Is there some underlying principle we have not discovered that makes this so?

Pi is not by any means the only interesting number of its kind. The natural base, e, is another likewise interesting number. It shares the same perplexing property of seeming to appear in unrelated realms. It is closely related to the Golden Ratio as well as is used to calculate simple probability problems.

Until recently, math was seen as the avenue by which long range predictions could be made about weather, the movements of the stock market, and other phenomena by which we could make a prediction if we only could gather enough data. Now, through the mathematics of chaos theory, we know that this less than interesting deterministic view of the world is unlikely. Through this study, beautiful artwork has been produced through mathematics (like the Mandelbrot Set) and new mathematical avenues of study have been opened. There will always be more. Of course this is true of all fields of study. I am just curious as to how many of you have paused just to reflect on the beauty of a field of study that may for some of you resulted in more drudgery than wonder. We have failed you if we have not ever brought this aspect of math before your eyes,