Will every PhD student from a reputed institute land a postdoc position? I have completed my master’s in pure mathematics in India.
Though I am passionate about mathematics and would really want to do a PhD in pure mathematics, one thing I am uncertain about is how would my life turn out after getting a PhD in pure mathematics.

I checked the departmental homepage of some reputed institutes and universities in our country to gather knowledge about their past PhD students.
I found that only a handful of them go to postdocs and a very few get recruited as assistant professors in other institutes.
There is no  information about the other students and I can't get any information about what they are doing.

My questions are:


Is there no guarantee to get a job after doing a PhD in pure mathematics?
Or it is that everyone will get a postdoc after getting a PhD in some institute?
Is a postdoc absolutely necessary after doing a PhD in mathematics?
Will I get a job after a postdoc in mathematics?


I am concerned because I don’t want to be among those who are without any work after doing a PhD.
There is a filter, surely.

Actually, at least in German system there are two filters: PhD → postdoc and postdoc → tenure/tenure-track.

But you are missing out one issue. Even if all people doing postdoc probably would like to get a tenure-track position (but do not), not all PhD students would like to get a postdoc. Heck, not all PhD students even finish their PhD! But the major point is: not all PhD holders want and do stay in academia.



Ok, you do want to stay in academia. There are three major issues:


Publications
Teaching experience
Funding acquisition.


The detailed answer is probably too long and too country-dependent, but typically you'd need these three major issues to be covered, if you want to land a tenure-track position.