I agree with Chinmoy! There are other civilizations too that are as old as ours, egs being Egypt, Greece etc. Another fact of life is that the Egyptians, Greeks etc. seem to have more respect for their ages-old monuments and are better at conserving them whereas we are busy destroying them and defacing them with vulgar graffiti!
There is another aspect to it.India the geographical entity as is known today was the creation of British rulers for administrative convenience and on the question of what is precisely Indian culture there could be a debate but what is undeniably true is that India's essence lies in cultural plurality which has evolved over a few thousand years or more.
India is one of the oldest civilizations. We find two distinct and separate streams- Aryans and Dravidian. Both claim to be oldest. Greek, Egyptian and Chinese are also very old. All these are prehistoric and it is not feasible to state which one is oldest.