Ask HN: What is the big idea with algorithms?

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].