I have recently finished my master’s in pure mathematics, and I wish to apply for PhD positions.
I had got the top grades of my classes (with a gpa of around 19.5 out of 20). Moreover, I am going to take a toefl test soon, and I think I will get a high grade.
However, the only issue in my doctoral applications is apparently the loathness of almost all of the university teachers who know me to write a letter of recommendation for me. On the other hand, every doctoral institution seems to require letters of recommendation.
Hence, my question specially to mathematics professors is, why do they require letters of recommendation when the level of mathematics (or a scientific discipline) of the applicant can be fairly determined by an interview?