PageRankPageRank

In the late 1990s at Stanford, two graduate students, Larry Page and Sergey Brin, asked a simple question: on a web of billions of pages, which ones are important? Their answer, PageRank, is named after Page, not after the web page.

The insight was to treat links as votes, but not all votes equally. A page is important if important pages link to it, a delightfully circular definition that turns out to have a clean mathematical solution.

They modeled it as a random surfer wandering the web, following links at random and occasionally jumping to a random page. PageRank is the long-run fraction of time this surfer spends on each page, which is exactly the steady state of a Markov chain over the link graph.

Computing it means finding that steady state across the entire web, a huge but tractable eigenvector calculation. Pages where the random surfer lingers are the ones that surface to the top.

Described in their 1998 paper on a large-scale hypertextual search engine, PageRank let Google rank results by structure rather than by keywords alone, and it beat the competition decisively enough to build one of the most valuable companies on earth.

Search has grown far more complex since, with many signals layered on top, but the founding idea, that importance flows through a network and settles into a stable distribution, remains one of the most consequential applications of Markov chains ever deployed.