Hearts of the mathematician, the astronomer and architect leap for joy: 91 steps on each of the four sides of the pyramid temple of Kukulcan lead heavenwards. Taken together along with the single top step, they total 365 - exactly the number of days in the year.
At the equinoxes in March and September there appears a unique phenomenon - at sundown the shadows of the pyramid platforms glide, snakelike, down the steps and join together on the stone-carved snake heads at the foot of the pyramid.
On the ballgame field in what is arguably the best-known and most heavily-visited Mayan site, the Chichen Itza, yet another aspect of the Mayas comes to light: A bas-relief shows a decapitated pelote player. Blood flowing from his throat takes on the form of snakes.
Does the sacrificial victim represent the victor or the vanquished of the game? Neither scientists nor local experts can say for certain. To this day the Mayas are a mystery.
As a result, particularly in this year the rumours about the Mayas are rife. Shortly before Christmas, on 21 December, the only Maya calendar known to date, comes to an end. The esoteric and conspiracy-minded crowd fear that this portends the end of the world.
But researchers don't go along with this. They say that for the Mayas, this date merely ends an important epoch, after which the circle starts anew. Scientists recently also discovered in Xultun, in north-eastern Guatemala, a Maya calendar that goes well beyond the year 2012.
Near Uxmal, a man named Antonio along with his brother runs a popular restaurant. They serve guests traditional dishes cooked according to original recipes. The cooking is done in an earthen oven sunk into the ground, the bottom of which is covered by glowing charcoal and hot stones. It is covered on top with a tin plate. Inside the oven, pieces of chicken and pork are broiled for four hours, until the meat absorbs the tantalising aroma of the local spices.
Asked about the end-of-time Maya calendar, Tony - as his friends call him - laughs it off. "End of the world? It's total nonsence. One time period will be ending and a new one will start. Life will go on.''
Uxmal radiates a special magic for the modest crowd of visitors. The so-called nuns' square above all is impressive for its bas-reliefs and facades.
If you're sitting on the upper platform of the governor's palace and let your view sweep across the site, then the only object to interrupt the thick, green tapestry of the rainforest now reclaiming a landscape changed by humans is the 35-metre-high tip of the prophet's pyramid.
The circle is closed in the coastal town of Tulum. Now once again back in the region of the holiday spots along the Riviera Maya, merchants and day trippers dominate the scene. Tulum belongs to among the last of the great sites of the Mayas.