Landau on Chess Tournaments and Google's PageRank

TL;DR

This paper explores Landau's 1895 relative scoring method for chess tournaments, highlighting its mathematical foundation and its influence on modern algorithms like Google's PageRank.

Contribution

It connects Landau's early relative scoring concept to its applications in modern network ranking algorithms, illustrating its lasting impact.

Findings

Landau's relative score concept predates and influences PageRank.

The scoring method considers players' strength, not just outcomes.

Historical analysis of Landau's work and its modern applications.

Abstract

In his first mathematical paper, published in 1895 when he was 18, Edmund Landau suggested a new way to determine the winner of a chess tournament by not simply adding for each player the fixed number of points they would get for each win or draw, but rather by considering the performance of all players in the tournament relative to each other: each player would get more credit for games won or drawn against stronger players. Landau called this "relative Wertbemessung", which translates to relative score. The basic idea from linear algebra behind this scoring system was rediscovered and reused in many contexts since 1895; in particular, it is a central ingredient in Google's PageRank.