The mystery of extraordinarily accurate medieval maps. The portolan maps of the 1500s of the Mediterranean were so accurate that ships today could navigate with them, while most earlier maps were useless for navigation and so imprecise that they are virtually unrecognizable to the modern eye.
Mapmakers left no rough drafts, no sketches, no descriptions of their work, but "John Hessler has approached the question using a tool that is foreign to most historians: mathematics. By systematically analyzing the discrepancies between the portolan charts and modern ones, Hessler has begun to trace the mapmaker's tracks within the maps themselves."
He discovered that different portions of portolan maps were rotated different amounts ranging from 6.5 to 11 degrees, corresponding to the different sailing records used to construct them. The sailing records consisted of lists of ports in the order that the ships encountered them, annotated with compass directions, sailing times between the ports, and sketches of geographic contours visible from afar, such as headlands projecting into the sea. Magnetic north is different from true north, and varies between places and over time at the same place, because of shifts in the molten iron moving in the Earth's outer core, which explains the 6.5 to 11 degree rotations of different parts of the map.