CONCEPT
Graph Theory
The mathematics of which things are connected to which—born in 1736 from a puzzle about seven bridges and now the structural substrate of every neural network, social platform, and routing table on earth.
Graph theory is the branch of mathematics concerned with the properties of networks: collections of vertices (nodes) joined by edges (lines), where the truth of interest lives entirely in the pattern of connections rather than in the size, shape, or position of the parts.
Leonhard Euler founded the field in 1736 by reducing the Seven Bridges of Königsberg to four dots and seven lines and proving that a walk crossing each bridge exactly once was impossible—not because no one had found it, but because the structure of the connections ruled it out. The result established that certain questions about the physical world can be answered entirely from their
abstract connection pattern, with every concrete detail safely discarded.
Neural networks, the backbone of contemporary AI, are graphs: units joined by weighted edges, with signal propagating across the connections. The internet is a graph of routers. Every social platform is a graph of people.
Large language models represent meaning as position in a high-dimensional