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I am a person who completed his master's last year and now I am preparing for PhD admissions in Europe. I am from a poor country in Asia.

I have 3 PhD interviews scheduled in last week of January to February for universities in France and Germany.1 interview is with prospective supervisor alone and 2 are with admission committee of 4-5 members.

Question: What exactly should I expect in PhD interviews of Pure Mathematics? Are questions related to Master's thesis asked? How long should I expect the length of the interview?

Any advice will be highly appreciated.

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The process is likely to be different in different places (even within the same country, or university), depending on the person interviewing you. I currently work in Germany. At the University of Bonn, the topology group interviews candidates together. The interview consists of a 30 minute presentation by the candidate, usually on their masters thesis, followed by 30 minutes of questions. The scope of the questions is informed by the presentation -- the first half is usually based on the talk, and the second half on general questions in topology, of the type we would like the candidate to already know before starting a PhD position. Sometimes we ask the candidate whether there are specific topics they feel most comfortable with, but usually this is clear from their application. Yes, we do ask the candidates to solve math problems.

Even within my university, the process varies from group to group. Others might just have a quite informal (virtual) conversation with the candidate, the talk component might be unique to the topologists. The length of the interview is highly variable.

My advice to you:

  1. Ask the person who invited you to interview what the planned format is and what you should prepare.

  2. Regardless of the answer, be prepared to answer questions about your masters thesis, your general area of research, and the direction you would like to pursue for your PhD.

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  • Just wanted to ask the following: I have done quite a lot of pure mathematics courses in my Masters which were heavy in proofs. I wanted to ask whether Prof.'s ask about proofs of results done in courses or just results. While revising, I revise only statements of proofs and definitions in a course. I don't remember a lot of proofs even of courses done in last semester ( 3rd semester). So, will it be a setback to me or not in the interview?
    – user135061
    Jan 29, 2022 at 15:45
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    A reasonable interviewer wouldn’t/shouldn’t ask about technical details of proofs, but questions about “ideas” of proofs of big theorems are on the table I think. (E.g. proof of the Seifert van Kampen theorem. I wouldn’t ask anyone to write down the details, but would like to know that they know the general idea).
    – Aru Ray
    Jan 29, 2022 at 17:13
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    But you should also consider proofs of the type you probably had to do in homeworks or exams, those are definitely on the table. Also, well known counter/examples.
    – Aru Ray
    Jan 29, 2022 at 17:14
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They will ask you about your research, your masters thesis (possibly also about your masters advisor), and whether you know what to expect from the PhD program. Usually, unlike interviews outside academia, they will not ask you to solve math problems. But they may ask you what classes you took.

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  • " They will ask you about your research" but I haven't started any research yet?
    – user135061
    Jan 19, 2022 at 7:24
  • " whether you know what to expect from the PhD program" I am expecting publishing 2-3 research papers and then join a good institute as post doc fellow. Is there anything else I should expect?
    – user135061
    Jan 19, 2022 at 7:26
  • If you have not done any undergrad research, you chances of getting into a PhD program at a good research University are slim. Publishing 2-3 research papers (or even one paper) in good journals would require a lot of work, and you seem to not expect any hard work.
    – markvs
    Jan 29, 2022 at 16:19
  • @markvs When you say 'research', do you mean original research or simply having learnt about the topic you want to study at PhD level? In the UK most people will be interviewed whilst part way through fourth year of an undergraduate degree, and they very often won't even have started their master's thesis by that point
    – Person
    Feb 11, 2022 at 0:41
  • @Person: By "research" I mean what here is called REU, research experience for undergraduates. It is usually done after the second or/and third year. It is an ordinary research which may or may not be related to future MS or PhD research. The point is that the interviewers should determine whether the applicant is prepared for PhD work and the applicant should show that (s)he is.
    – markvs
    Feb 11, 2022 at 1:12

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