Timothy Gowers on the importance of mathematics, found from The Trans-Siberian Handbook. (There's a video version, too, which I haven't watched, because I can read faster than I can watch video; a link is in the TSH post.)
At The Dilbert Blog, Scott Adams writes:
My reason for majoring in economics in college was to understand how the world works, so I would be more equipped to navigate in it. I think it was a good choice. Has your college major given you any mild super powers?
Somewhat jokingly, I replied:
I majored in mathematics and am a PhD student in mathematics now. This gives me the super power of making people I don't want to talk to at parties go away, because when they hear I'm a mathematician they generally assume we have nothing in common.
This is true to some extent. I also find that it has the reverse effect -- it makes people I want to talk to at parties come to me, because for some reason the people I find most interesting are the ones who will respond to "I'm a mathematician" with "I always found math really interesting but I'm not any good at it." These people are usually interesting to talk to, perhaps because they haven't had the fun beat out of them by a technical education.
Here's Thomas Maarup's masters' thesis on the game of Hex -- the history of the game, the classic proof of the existence of a winning strategy, the complexity, and some tips on how to actually play the game. (The proof that the winning strategy exists is nonconstructive, and exhaustive search would take too long for practical purposes.)
Some notes on the calculation of the gamma function.
Graph Visualization is Difficult, but is it Useful? from Data Mining: Text Mining, Visualization and Social Media
And the game of "nuclear pennies". It turns out that the strategy to this game is related to the isomorphism of 7-tuples of trees with individual trees, which I've written about here before (but I can't find that post). The existence of such an isomorphism is hinted at by the fact that if you take a generating function for trees, f(z) = (1-(1-4z)1/2)/(2z), you have f(1) = ω where ω is a primitive sixth root of unity; thus ω7 = ω, and it seems just inside the realm of possibility that 7-tuples of trees and trees might count the same thing. From this I learned about the paper of Marcelo Fiore and Tom Leinster, Objects of Categories as Complex Numbers, which says basically that this idea can be made rigorous.