In 1736 Euler proved that it was impossible to walk through the city of Königsberg crossing each of its seven bridges exactly once. In doing so, he invented graph theory — the study of networks as abstract structures of nodes and edges. This was mathematics applied not to numbers but to relationships.
Euler's work on partitions, permutations, and graph enumeration laid the groundwork for modern combinatorics. His formula relating the vertices, edges, and faces of a polyhedron (V − E + F = 2) revealed deep structural invariants — properties that persist regardless of how the structure is deformed.
Modern network analysis, supply chain optimisation, and social graph algorithms all descend from Euler's graphs. In quantitative finance, graph structures model relationships between companies, sectors, and financial instruments — the topology of the market.
Our embedding space maps companies as nodes in a high-dimensional graph. Similarity, clustering, and anomaly detection are all graph-theoretic operations. Euler gave us the language to reason about structure and connection.