From the bridges of Königsberg to the fields of Alzheimer

Abstract

Connectomics, the comprehensive mapping of all neural connections in the brain, is an emerging field with great promise.1–6 To better understand the puzzle of how these connections are organized, connectomics has recently turned to graph theory, a branch of mathematics developed in the 18th century by the Swiss mathematical genius Leonhard Euler to solve the problem known as the Seven Bridges of Konigsberg.4–6 Konigsberg, Prussia, was a city on the Pregel River with 2 islands linked to each other and the mainland by 7 bridges.4 The challenge, to find a continuous path that crosses each bridge exactly once and returns to the starting point,4 was solved by Euler, who determined, using graph theory, that it was mathematically impossible. In more recent times, scientists have used graph theory to probe the weaknesses of the New York City electrical power grid, the social network of the Screen Actors Guild, and the spread of happiness in the Framingham study cohort.4–6 The successful reconstruction of all neural and synaptic connections in Caenorhabditis elegans , followed by partial reconstructions of a mouse visual cortex, has naturally led to great interest in the human brain connectome.1,5