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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?

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    Why don't people want to write on your behalf? – Buffy Jan 1 at 13:25
  • One of them said she’s on a leave so she couldn’t. Another one said he would do it if I had taken at least two of his courses. Another one did not answer my email. – user117892 Jan 1 at 13:29
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    May i ask how did you get into the masters program? – scaaahu Jan 1 at 14:34
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    It was through a mathematics test @scaaahu – user117892 Jan 1 at 14:38
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Most universities want some independent advice about candidates. This should come from people who know the candidate and can attest to their suitability and likely successful outcome. It is hard to gauge that with material provided only by the candidate, even in an interview.

And there is more to graduate school (or a job, for that matter) than raw competence. There is a social aspect and so a desire to accept people who will get along well in the program or job. (That is why I asked the question in the comment, actually.)

But it is what it is, so in your case, you just need to live with it. I'm surprised that few teachers know you, actually. Think about others who can help. But I would keep trying with the three that you mention in the comment. Let them know of your need and the difficulty of finding others to help.

  • I’m in general introverted and not ubiquitous unlike almost all students. – user117892 Jan 1 at 13:43
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    Actually introversion in mathematicians is ubiquitous. Almost a badge of honor. But you can learn to act otherwise when needed. Introversion isn't a personality flaw. But sometimes you just need to put yourself out there in the mix. You might not recognize it from my writing on this site, but I'm also very introverted. – Buffy Jan 1 at 13:49
  • Thanks for your suggestion. Also I am working on my first mathematical paper to obviate this problem – user117892 Jan 1 at 14:00
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    “Actually introversion in mathematicians is ubiquitous. Almost a badge of honor.” Certainly NOT in my experience. – Eric Jan 2 at 2:33
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    @Eric, not exactly. You do point out some cautions that introverted people need to be aware of, but I was more speaking of the problem of the brilliant person who is also a jerk and doesn't get along with anyone. I am, myself, very introverted and got a doctorate (math) and had a great career, though I switched to CS. But I learned how to act "in the world" so that introversion wasn't a problem (eventually). It is a learned skill like many other things. Introversion isn't destiny. – Buffy Jan 2 at 15:44
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About the interview part. It is true that mathematical skill can be determined by an interview. Also the language skills can be somewhat determined by an interview. The truth is that interviewing each candidate would take a lot of time. Even scheduling interviews for every single candidate would be a mess. Same for reading previous publications / thesises. With the volume of applications each university is getting, it is practically impossible to investigate each application in depth. Also, as Buffy mentions, there are social aspects to a candidate which cannot be measured by a single interview. At least not completely. Similarly I do not think an interview would accurately gauge someone's mathematics abilities. At least not every single time. An interview puts the candidate on the spot and it is a high stress situation. Many are effected negatively by that.

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