what did the mayan indians contribute to modern day society?

They provide jobs for Archaeologists, Anthropologists, Art Historians, and History teachers, like the one who assigned you this question.

Mayan Contributions To Modern Society

Sorry Richard, the Julian Calendar (and the later Gregorian Calendar) was a 365 day with extra day every 4 years calender at least 600 years before the Mayan Haab derived calendar of 360 days. The Long Count Calendar simply calculated days into the past, and was very accurate, but it was not in common use by the daily people. Also, the Long Count Calendar to which you refer was independent of the solar calenders traditionally used in Europe and Asia.

As already said, they provided much employment for historians and the like, but not much that influences the modern cultures.elsewhere in the world.

There is a modern tendency to glorify this civilisation, just as Rennaissance Europe often glorified the ancient Greek and Roman cultures.

Theres any essay of Bertand Russell about the uses of history... Maybe you find a good answer there. Have you read Jorge Luis Borges? In one of his stories he makes a good trick: The hero of a revolution could be the worst traitor, so you will never know. History could be false. But it has an use... I belive it makes your more skeptic... and the good and bad examples of the past give you some light into deep questions: who we are your are and where are the boundaries of men. There is also a sentiment of the real. When I read about Fouche I could understand what politics is in my time, there are some histories about what goes always in society. And that feeling, history!

I do believe they invented the most accurate calendar, far more accurate than what the civilized world was using.

http://www.mayanindians.com/