Washington - John Hessler, mathematical wizard and the senior cartographic librarian at the Library of Congress, slipped into the locked underground vaults of the library one morning last week.

Hessler approached a priceless 1559 portolan chart on the table before him, sketched in the hand of Mateo Prunes, the Majorcan mapmaker. The nautical map of the Mediterranean and Black seas is inked onto the skin of a single sheep.

It is a rare representative of one of the world's greatest and most enduring mysteries: Where and how did medieval mapmakers, apparently armed with no more than a compass, an hourglass and sets of sailing directions, develop stunningly accurate maps of southern Europe, the Black Sea and North African coastlines, as if they were looking down from a satellite, when no one had been higher than a treetop?

No known predecessors

The earliest known portolan (PORT-oh-lawn) chart, the Carta Pisana, appears in about 1275 - with no known predecessors. It is perhaps the first modern scientific map and contrasted sharply to the "mappamundi" of the era, the colorful maps with unrecognizable geography and fantastic creatures and legends. It bears no resemblance to the methods of the mathematician Ptolemy, and does not use measurements of longitude and latitude.

And yet, despite its stunning accuracy, the map "seems to have emerged full-blown from the seas it describes," one reference journal notes. No one today knows who made the first maps, or how they calculated distance so accurately, or even how all the information came to be compiled.

"The real mystery is that if you took all the notebooks from the sailors used in making these charts, along with the coordinates and descriptions," Hessler says, tapping the glass that covers the ancient vellum, "you still couldn't make this map."

Hessler, 49, is one of the world's leading experts in trying to decode the mysteries of the maps, and presented some of his intricate research at a recent conference at the library, "Re-Examining the Portolan Chart: History, Navigation and Science."

Sponsored by Philip Lee Phillips Society, the fundraising arm of the library's Geography and Map Division, it drew about 200 academics, donors and collectors to a daylong session that presented the ancient mystery of the portolans (from the Italian word for "ports"). It was one of those moments in which Washington, D.C., invariably portrayed as a dry city of faceless bureaucrats, revealed itself as a place filled with people who could, with a little fictional help, just as easily be the basis for a ripping good thriller.

"People think maybe the Romans made the first ones and they've been lost, or the Phoenicians, or even aliens," says Evelyn Edson, author of "The World Map: 1300-1492," and one of the conference's speakers. "It certainly seems related to the introduction of the compass, in the 11th century. But there's nothing at all to explain how they were made. ... It's been very tempting for people over the years to try to make up the answer."

"The ancient Greeks and Romans had traditions of mapmaking; there's Ptolemy, and there's a line of progression," Hessler says. "But here, it just explodes out of nowhere. It appears to be a true invention of the Middle Ages."

Mathematical research

Hessler's means of research isn't cultural or nautical - it is entirely mathematical. He has taken 22 of the few hundred portolan maps known to be in existence and measured them against modern maps of the same area. He uses, say, 100 points of comparison on each map and then applies complicated algorithms to calculate the differences between each point on each map.

Hessler compares these two maps on a computer-modeled overlay, with the scale of error then plotted onto a "deformation grid." He is then able to see where the charts were more accurate and where they were less accurate, from which he infers where sailing and close observation took place, and which areas were more loosely charted.

This, in turn, reveals more about the birthplace and methodology of the map. For example, the maps were good in the various seas of the Mediterranean, but terrible once out in the Atlantic, rounding up to the British Isles.

Still, they were reliable guides to the known world for 400 years, and they have concealed the secrets of their origins and methods for another four centuries, leaving the answers to the realm of novelists and storytellers.