Abstract: Why is Google so good at what it does? There are a variety of reasons, but one fundamental thing that distinguishes Google and has put them so far ahead of other search engines is their patented PageRank concept. PageRank has revolutionized Web search to the extent that it has been charged in Federal Court with driving the direction of commerce on the Internet. Many mathematicians are therefore surprised when they learn that a technology of such consequence is predicated on the same mathematics that is available to undergraduate students. This talk will survey some of the scientific concepts behind today's major search engines including Google and Ask.com.