One of the most populous metropolises on the planet, Mexico City, stands atop the ruins of the 15th century Aztec capital Tenochtitlán. The two may not appear to have much in common, but according to a new study they obeyed the same mathematical formula. Scientists have found that—despite major differences in culture, government, and technology—the productivity of both ancient and modern cities grew faster than their populations did. The finding could lead to ways to improve the efficiency of today’s urban centers.

“I think it’s great work,” says archaeologist David Carballo of Boston University, who was not involved with the research. "The fact that this is suggesting that there are some … trends in how settlement works I think is a message for contemporary urban planners."

After scientists observed this pattern in modern cities, archaeologists wondered if the trend would hold for ancient ones as well. Researchers led by archaeologist Scott Ortman of the University of Colorado, Boulder, combed through archaeological data describing thousands of ancient settlements established over 2000 years in the basin surrounding modern-day Mexico City. The inhabitants of this area were accomplished architects, constructing massive pyramids and temples, many of whose ruins remain. Because the material possessions of the inhabitants had been lost to the ages, researchers used a proxy for the productivity of each settlement—the number and size of such monuments and of villagers’ homes.

In larger ancient cities, there were more monuments per person, and houses and monuments were larger, the team reports today in Science Advances, meaning that the cities received a productivity boost beyond that provided by the increased number of workers. The trend was evident across a wide range of settlement sizes—from villages of a few hundred people to capital cities of hundreds of thousands: the larger the city, the bigger the boost.

Superficially, ancient cities have little in common with today’s technology-driven metropolises. Tenochtitlán had a population of about 200,000 people, a bustling marketplace, and a grid of busy roads and canals. But it had no modern technology, no beasts of burden (let alone mass transit like that available in modern cities), and an economy based heavily on agriculture. Yet certain aspects of human social life—like the way people interact with and depend on one another—apparently remained the same throughout the ages. Despite the vast differences across time, the researchers were able to model modern and ancient cities’ higher productivity with the same mathematical equations. That may be because in any large city, you don't have to go far for a social interaction, so it is easier to gain from your neighbors.

“To me, the idea that the same fundamental processes that generate a place like New York were operating in ancient farming villages in other parts of the world is just astonishing,” Ortman says.

“Because of this body of research, I think we’re closer to understanding cities in a fundamental way than we were previously,” says archaeologist Michael Smith of Arizona State University, Tempe, who was not involved in the work.

Understanding how cities function might help us improve them, the researchers say. Studying different types of ancient urban centers, for example, could help architects construct public spaces that help people interact more easily and infrastructure that will simplify movement throughout the city.