The history of Bharat Natyam is interesting.  The genre of Bharat Natyam was developed by amalgamating a number of elements from the earlier forms of Dassi Attam and Sadr.  Dassi Attam was a dance form of the Deva Dassis (temple dancing girls) while Sadr was a form found in the palaces of southern India.  A number of people contributed to the development of Bharat Natyam, but the most notable was E. Krishna Iyer of Madras (Chennai).  This was in the 1930's

It is difficult to determine the age of Bharat Natyam; this is due to the evolving nature of Indian dance.  Although Bharat Natyam evolved from Sadrand Dassi Attam, there are differences.  If one feels that Bharat Natyam is different enough to be considered a distinct genre, then we may safely say that it is only about 70 years old.  On the other hand, if we consider the differences to be insignificant, then we may push the age back several hundred years.  However, the careless manner in which many artists date Bharat Natyam back to the Natya Shastra is absolutely preposterous.  The cumulative changes that have occurred over the last 2000 years make such statements totally insupportable.