How to do a PhD to equip myself for a job as assistant professor This is in reference to my older question: Will every PhD student from a reputed institute land a postdoc position?.

I have completed my master’s in pure mathematics and have got a funding for five years.
I have been told that there are few faculty positions available w.r.t the number of PhDs generated (I don’t know if its really true).

My questions:


How should I plan to do my research in order to get an edge over the others in getting a job?


Should I try to visit some famous universities (see if they accept me) and work with some very good advisors so that I get to solve a very good problem?
Should I try to get a breakthrough result even if  it takes seven to eight years and complete my PhD in that? Because completing your PhD in less than five years and having no major result will push you back.



In other words how should I prepare myself to be better equipped in landing a postdoc and then a job as as assistant professor? 

I am asking this because, no matter how passionate you are about mathematics, you need to find a job some day or the other to run yourself and your family.
It is true that there are far fewer postdoc positions than graduates with a PhD. So it is legitimate to ask what you can do to improve your chances to eventually get a postdoc position, and from there on a faculty position.

The problem is that the number of factors that influence whether or not you will end up with one of these positions is large. There are some obvious ones:


If you get a PhD from a good university, that helps.
If you have a famous adviser, that helps.
If you are substantially better, that helps.
If you work in a field with current excitement, that helps.


Of course, there is also the issue that if you work in a field that is "hot" but that you don't enjoy, you're probably not going to do well.

Many of these factors are either out of your control (admission to Harvard or Berkeley) or that you can't foresee with your current knowledge, given that you haven't been involved in research for too long. But, if you get admitted to a good university, take the position and go from there.

(I will note that -- having read maybe 500 grad school applications in math -- about 2/3 of grad school applicants want to eventually become professors at a research university. This is wildly unrealistic -- I don't know exact numbers, but would imagine that overall only maybe 10% of grad students will eventually achieve this. I'm telling you this because you will have to contend with the fact that basically everyone around you has the same goal as you: they all want to go to a good university, be advised by that famous professor, etc. You'll have to work hard to be better than all of those others.)