Another justification of the PageRank algorithm is that hyperlinks influence the index of a page. For example, if a page is referred to by multiple other pages (well cited), then it's deemed important and will have a higher PageRank.

It assumes there's a random user click on pages at random and not backtracking. The probability in the randomness is the PageRank.

The damping factor is the probability that the "random surfer" will get bored and move on to another page. The damping factor can personalize search results, making it difficult for people to manipulate the system in order to get a higher ranking.

Another goal of Google is a specification of the previous goal (improved search quality), as they want to create an improved searching experience for students.

The World Wide Web was originally created to facilitate academic research, and Google plans on creating a system that can support research activities as mentioned.

The biggest issue with previous Web Search engines, like the World Wide Web Worm and later Altavista was that they handled very limited queries per day. They ranged in the millions, starting from 2, 20, to 100m, which was expected because of the technology, but not the most efficient manner.

What Google proposes is the challenge of a search engine with efficient crawling technology, able to use storage efficiently, fast queries and sorting, etc. It's inevitable that the tasks will become harder as the demand for the Web increases, but Google is designed to be scaled to large data sets.

Improved search quality means that users searching can find exactly what it is they want. At the time, search engines weren't reliable and it was more than a myth for a search engine to find "almost anything on the Web".