This is not a scientific linguistic paper; I am just trying to contradict the false claims by the Hindutva walas and other Indian ultra nationalists.
Once upon a time there lived a group of people somewhere on the southern end of the Ural, who spoke something that we shall call proto-Indo-Germanic. Some of these people started moving to the east and other started moving west. Wherever they settled in sufficient numbers, they and the original population of the area ended up speaking some kind of mix between proto-Indo-Germanic and the local lingo.
This movement of peoples was not a linear event of groups moving at a steady pace and all the time. One generation might move a hundred miles and then settle. Some of these settlers might take up sticks again in the next generation, the generation after that or the one after that.
If these people were hunter-gatherers or cattle herding nomads, they might be on the move most of the time, moving to and from areas with good grazing, good overwintering etc, and if this was not available locally they would move more to the west or more to the east.
Do you get the picture ? In this way those that went west ended up in Europe, as far as Ireland and Iceland, and eventually substantial numbers also settled in the Americas, Australia and New Zealand and Southern Africa, enough to be either in the majority or to be the ruling class.
This article concentrates on the groups that ended up on the South Asian sub-continent. Most of the people that they met upon arrival were probably Dravidians who earlier had reached a high pinnacle of civilization in places like Harappa and Mohenjo-Daro, but whose culture was past its prime. The vigorous cattle herding Indo-Germanics might have been less ‘civilised’, but they conquered the Dravidian states.
The Indo-Germanic languages, based on Sanskrit or whatever it was that proto-Indo-Germanic had evolved into by that time, still dominate the north of the sub-continent, while in the south Dravidian languages are spoken.
These ‘relatives’ of the Dravidian language(s) of thousands of years ago of the north west of India have been influenced by Indo-Germanic languages.
The modern sub-continental languages of the north of India like Hindi, Panjabi or Gujarati have been influenced by the ‘Dravidian’ languages.
Summing up : Sanskrit is an ancient language, but it is not the mother of all languages. Dravidian languages, most languages spoken in China or South East Asia, the Amerinder languages, the Basque language all are most definitely not off-shoots of Sanskrit or of any other Indo-Germanic language.