Firstly, I'm a non-CS major and am much unlike many of you mathematical whiz kids who make up this board, so having stated that, I hope you'll get a better idea for why this book I just checked out at the library, Algorithms in a Nutshell [http://oreilly.com/catalog/9780596516246/], gets me so hot.
To me algorithms are as interesting as the formulas that makeup our Universe brought to us from physicists, granted they're both inspired from the same basis, which is to express a set of quantities algebraically that hold true as a solution to a problem. However, physicists and computer scientists are both working towards opposite ends, since physicists attempt to generalize a set of observations from the physical world into a law, computer scientists attempt to materialize a set of observations from the abstract world into a set of instructions, called an algorithm.
When I open this text-book's ToC it reads like a road-map into the beginning of the mostly unknown Universe of computer programming. I want you to briefly summarize why algorithms are so important, where they came from [their genesis], how you use them on a daily basis, whether or not they're more important than design, and what the formulas of the future will do for humanity.
[EDIT] More bluntly, summarize [and categorize, if you'd like] the evolution of algorithm design starting with insertion sort and ending at your heart's content [or AI].
AIT and computational complexity theory arguably underlay all other sciences. They allow us to define randomness (http://www.cs.auckland.ac.nz/~chaitin/georgia.html), pattern, probability (http://www.scholarpedia.org/article/Algorithmic_probability), inference (http://www.wisegeek.com/what-is-solomonoff-induction.htm), ignorance, and perhaps one day consciousness.
They allow us to prove, with absolute certainty, whether we are talking to a deity ( http://scottaaronson.com/blog/?p=56), and to prove that some questions will forever be beyond our grasp.
Even discounting Zuse and Wheeler's "It's from Bits" conception of information and computation as the basis of physics (http://en.wikipedia.org/wiki/Digital_physics), these disciplines promise to help us solve our hardest and most interesting problems by, first of all, telling us whether they are solvable at all, and if so, whether they are solvable before the heat death of the universe. Consider that Goedel, Cohen, and Turing struck down the Continuum Hypothesis from Hilbert's list of open problems, allowing us to abandon a futile line of inquiry and focus on other problems. Current developments in quantum computability theory may similarly strike down vast swathes of sterile ideas, directing us toward questions whose answers are solvable.