I am a graduate student in mathematics. I've been having a difficult relationship with my advisor, and I need some help on the matter.
Some background
When I just started my graduate studies, my advisor warned me that he tends to be strict, and that sometimes he can have anger outbursts. I thought (and still think) that a strict advisor would be good for me, and didn't think the mentioned anger issue would be as bad as it turned out to be.
In the beginning, our relationship was good and (professionally) friendly, and I looked forward to every meeting with him. Our discussions gave me motivation in my studies and research.
About half a year later, I was going through depression unrelated to academic issues (and started being treated by medications), and was completely unproductive and not concentrated on my work for a few of months, which my advisor was unhappy about. He said that he didn't care about my personal problems, didn't want to hear excuses, and that he expected me to work regardless. From that point on, our relationship completely changed. He stopped being nice and supportive, and started accusing me of not being serious and not working hard enough. This seems to have been the main trigger for his behaviour which I am to describe next.
The problem
If I don't get results, and try explaining that I've been working hard and just couldn't come up with a solution, my advisor starts yelling (yes, really yelling) that my progress is too slow, that he's sure he could have solved it in a month/week/hour himself if he tried, etc.
He also tends to interpret everything I say as a personal accusation, even though I always try to formulate my questions carefully and politely. For example, if I ask whether I should stick with a certain approach even after being unsuccessful for a while, he responds by yelling that he's an experienced researcher and that if he suggested it there must be a reason, and how dare I, a student, question anything he says.
A similar situation happened when I pointed out a mistake made by another researcher (and which was checked, per my request, by a third party after the incident). My advisor didn't check my claim thoroughly, and yelled that how dare I "accuse" a well-regarded researcher of making a mistake, and that it makes him angry that I "don't check my facts" before making such a claim, and compared me to mathematical cranks.
[To clarify: I pointed out the mistake in an email to my advisor, not in any arrogant way, and without involving anyone else at that point.]
It is difficult for me to work, because every time I'm stuck on something, I panic thinking about our next meeting and how he would yell at me again for lack of results. It also makes me look for "shortcuts" instead of really understanding what I'm studying for my research (even when those are basic things that he would agree I should understand) to save time.
When I explained to my advisor that this slows down my progress, he said that he's not a psychologist, and it's not his job to deal with my psychological problems.
Another problem is that almost all of our conversations revolve around my lack of progress and him yelling repeatedly the same things, while I'm trying to pull the conversation back to the math, as I need his help, and as there is no-one else working in this area at my university (and perhaps in the country). He had another graduate student who just graduated and switched to a different field, telling me that he would not continue for a PhD with this advisor because "he can't survive this psychological pressure for several more years".
I don't see a feasible option of switching advisors for the reason stated above, and also because based on his past PhD students and on what he told me, he could significantly help me in finding positions after I graduate. Also, I regard him as a good advisor in other aspects (much better than other advisors I know at our department), and I do believe that after all he cares and would help me if I made progress.
As much as possible, I would like to have a good relationship with him, and I definitely don't want to harm him in any way (such as reporting it - which would have been counter-productive anyway).
Our relationship quite reminds me of the movie "Whiplash" (without the physical abuse)...
Since the situation seems to have been worsening recently, I would very much appreciate some input on how to deal with this situation.
Answer
I cannot stop typing this long response.
I'm sorry to hear that you are in this situation and I have lots of sympathy for you. Your story sounds similar to but not as horrible as mine in the previous university and the department I was in (NOT the one I list in my profile now, that is the one I'm currently in, the one I enjoy so far). I'll first give you a one line advice, then answer your question in detail. In the end, I attached my story just for your reference (can't resist telling it!).
One-Line Advice
Most likely, the best option is to peacefully walk away and find a new advisor.
Detailed Answer
Based on your description, I can hardly imagine things will be better later on if you don't take action now. You've worked reasonably hard, but have slow progress for the reasons you don't have control. There are many misunderstandings in the communication with your advisor, and most importantly you're scared of meeting with your advisor. It's impossible to produce any good research work under a scenario like this. Time to look for someone else that fits you better.
You do not specify which stage of graduate study you are in. This may affect your approach now. If you are in the early stage (before passing preliminary/qualify), you should simply walk away, pass the exams, claim your interest change and convince someone else to be your advisor. It's not unusual at all for students to change advisor at this stage. If you're in the late stage (all but dissertation), you might consider enduring the pain for another year to get your degree, the potential cost (like dropping out) of making any unsuccessful move is too huge at this stage. If you're in the middle stage(pass qualify not yet advance to candidacy), the situation is awkward. You probably should talk to some department/university authority, and find out what's the best way to continue your study. However, you need to be very careful about who you talk to and how you talk.
When you describe your scenario to any third party (other professors, department chair, ombudsman, etc.), focus on the key issues you're facing and give them enough information so they can offer reasonable solutions. Avoid ranting and complaining, even if what you're saying is absolutely correct and can provide evidences. You run into danger of convincing other people you're a lazy student with many excuses. For example, you should avoid suffering the things I suffered (see my story+rant).
Last but not least, when it comes to advisor, you should have doubts on words of senior students and most recent graduates, they are the people who rely on advisor's letter to find jobs, therefore are unlikely to tell you any bad words, even if they don't like the advisor themselves.
End of Detailed Answer
My story+rant (only for reference)
Almost the same structure as your story, three years ago I was a new graduate student (in Ph.D. program) working in computational chemistry. It was OK in the beginning. About a few months later, I found out the software and source code I was supposed to use to do the calculation of my main project was fundamentally flawed. Some physical quantities were calculated on a non-trivial wrong way and it was clear to me that any data outputted would be meaningless unless the problems were fixed. I temporarily stopped working on the project to resolve the issue with my collaborators (one postdoc., one software engineer). It was a much slower process than I expect, because the person who wrote the code, although an expert software engineer, knows relatively little about the research I did and couldn't understand why the code was wrong for a long time.
My former advisor then behaved the way like your current advisor. In our meeting, he ignored the issue I faced and only blamed me on slow progress. Very often I found the suggestion he made was wrong and the solution I figured out myself was right. Whenever I pointed out the errors in other papers, providing more than sufficient evidences, he thought I must make up excuses for failing to reproduce the result in the paper. When I wanted to pull the discussion back to the research and seek for advises, all I got is "This is not undergraduate, you're supposed to figure it out."
After many meetings like that eventually he kicked me out of the lab(where he had already kicked out more than half of his students for many different weird reasons), originally with the promised of funding me finishing masters. He gave my research project to another student. Later on he blocked my access to all the data I had, and requested me to come back to lab if the student continue on my project had any problem, otherwise he was going to cut the funding. Even worse, I worked as a TA of my former advisor the academic quarter he kicked me out of his lab, he simply found every chance I made an insignificant mistake in TA job to blamed me, and sent abusive emails.
(Here is what I did, and don't want you to repeat) Finally, I cannot endure many abusive emails like that, decided to response one of them rudely (no personal insult and threat though), accused him lying and attached with evidences. The email was cc to all his group members and some department faculties and staffs. He was scared, he turned into the graduate community center (something equivalent to counseling center), described me as a potential criminal, and asked them to physically isolated me from the department. It took a while for me to convince them that I was the victim, not the other way around. After a few weeks of long conversations via the third party, we finally achieved some compromise- He agreed to do what he promised originally (fund me 2 more months to finish M.S.).
On the other hand, despite the evidence, it was impossible for me to convince other faculties in that department to be my new advisor. Most of them believed my former advisor's words and thought I was a failing student with excuses. They set up an "advancement exam" for me, at the date one faculty who potentially supported me had a doctor appointment, to find an official reason to kicked me out of their Ph.D. program.
End of my story+rant
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