Q:

Requesting the mentor regarding the PhD research topic selection

One of my friends is doing PhD under a good faculty from one year. 
The mentor wants to give PhD only if the student writes two papers in SCI journals. The student wants to do his PhD on number theory conjectures. The mentor is saying that the PhD and groundbreaking research work are independent and hence the mentor saying my friend to work on small incremental work that will give papers quickly. 
How to make it allowed to work under the same mentor (mentor is good enough and one year completed)?  

A:

It is a mistake for most students (Ramanujan excepted) to go against his or her advisor. I'm sure that the advisors complete thoughts are more complex than you present here, but probably involve the risk of taking on a big project as a student and ending up with nothing - no results and no degree. Some problems are hard and take years-decades-centuries to resolve. 
The advisor is giving good advice and following it will put him or her on the side of the student. 
If "your friend" wants to take on the big project there is no problem, but will be working from a stronger position by finishing the doctorate first. 
Take the advice. It is the faster path to success. 

