Hi,

It is not essential to join IISc, IISER, ISI to pursue research in the field of Mathematics, be it or any other. You can obviously go for research by pursuing Doctorate degree in top universities like Banaras Hindu University, Delhi University, Jamia Milia Islamia or any other. There is no restriction as such.

So, you can certainly choose these top universities for pursuing research in your concerned subjects.

You can check for PhD/Research in Mathematics Universities from the following page: https://university.careers360.com/colleges/list-of-phd-in-mathematics-universities-in-india