How do you reconcile mathematical genius with a bloodthirsty penchant for human sacrifice? This paradox lingered in my mind as I explored a stretch of Mayan ruins in Mexico's Yucatan peninsula. Fifteen hundred years ago, the Mayan people erected temples of religious and astronomical brilliance born of an exacting logic. They placated the gods with a steady stream of human blood. Climbing each temple step, examining stone carvings of magic and monsters, I was confronted by an ancient conflict between reason and faith so extreme, I could only wonder, Why? How?

A wall of skulls at Chichen Itza

Nobody knows for sure. Your best bet is to bring a hat, a couple liters of water, and your hiking shoes to explore the question for yourself. There is no substitute for being there—feeling limestone facades aged by the sun and rain; watching the forest stretch away endlessly in all directions from the top of the Grand Pyramid or El Castillo; sitting silently in a courtyard beneath the shadow of a great temple.

To see all the ruins of the Yucatan would take weeks—months even. There are many ways to go about it, many choices to make. The complexes at Chichen Itza and Palenque are world-renowned—and infested with hordes of tourists. Some equally beautiful but more remote sites provide solitude, mystery, and a deeper resonance with the ancient Mayans.

One such trip is called the Ruta Puuc (or the Puuc Route), located in western Yucatan State. This 30-mile stretch of paved highway through hills (Puuc means "hills" in local Mayan language) and forest yields several temple complexes and one of the most spectacular cave systems in the world—Grutas de Loltun. The largest of the ceremonial sites, Uxmal (pronounced Oosh-mal), was one of the major religious and political centers in the Mayan world.