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Most people think Google’s original success was about searching for keywords. They’re wrong. The real secret—the mathematical insight worth over $25 billion—wasn't about what was on the page, but how the pages connected to each other. In this deep dive, we visualize PageRank: the algorithm that organized the chaos of the World Wide Web using nothing but Linear Algebra. We move beyond the simple "popularity contest" metaphor to understand the true mechanics of the Random Surfer, Stochastic Matrices, and the Eigenvector that defines modern information. How This Video Was Made: This video was created using a custom application I developed that automatically converts technical documents into high-fidelity educational videos. By parsing the text and math, the app generates the script, storyboard, and renders these animations. Original Source Document: This visualization is based on the paper "The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google" by Kurt Bryan and Tanya Leise. Read the full paper here: https://www.rose-hulman.edu/~bryan/go...