Where did I lose control of my studies?

Question

I am a 5th MSc semester mathematics student at a local German university. Since fall, I have been working on my thesis, which is the only remaining task for finishing my studies.

I had not had particular difficulties during my studies, apart from the usual struggling and doubts I suppose every student undergoes: before my masters studies, I had spent 7 semesters at another university on two BScs in physics and mathematics. I am paid by a public scholarship. I had decided to change the university for my master's half for personal reasons and half in order to have a greater choice in courses held. My average score is 1.5 at the moment, which also had been my final score for the two BScs.

Now that I have started my thesis, nearly everything has changed: I am working with a professor whose courses I took several of, all with good grades, so she did not object to supervising my thesis. Although I have not had severe problems with my studies before, I am getting nowhere with my work now:

For understanding a single paper I am supposed to work on I sometimes need weeks, let alone the questions posed to me to think on, which I sometimes spend weeks without any serious results I could present. I have the impression that I am lacking creativity, intuition and a sufficient knowledge which I think I should have acquainted during my courses.

My problems have driven me into particular personal problems: I have lost contact with most of my former colleagues I used to spend every weekend with, partially because they seem to have lost interest in spending time with me, and partially because my mind is governed by thinking of my inferior scientific performance and the conviction no one wants to have to do with such a poor student. I cannot enjoy leisure time since I permanently have to think of the open problems that haven't worked out over a long time. I cannot claim to have chosen a university where I am competing with the best.

For 1½ months I have been taking antidepressives and having psychotherapy, which barely helps to soften the biggest peaks of auto-aggression and contemplating self-harm, but have not yet helped me to find another view on what I'm doing.

TL;DR

Although my university performance seemed sufficient for me not to worry much about it, starting working on my master's thesis has revealed a vast lack of mathematical knowledge and poor mathematical working capabilities. The longer I work on it, the more I lose any self-esteem.

Question: Where should I have foreseen my problems? Which signs did I ignore? Where did I miss to put things on the right track? And: how shall I find value in myself, now that I have found myself incapable of pursuing research, and have lost everything else?

Answer 1

Nothing you've described sounds like a serious academic problem. Taking weeks to understand a paper, and working on a problem for weeks without results, are entirely normal in research mathematics. And there is always a large gap between what you learn in coursework and what you need for research.

Trying to get better by just working harder or longer can be counterproductive. It is important to spend time on other things, even when you feel like you're way behind.

Clearly you have some problems with mental health right now. I'm not qualified to advise you on that, but it's good that you're getting professional help, and it's only been 1.5 months - such issues don't usually get "cured" as quickly as that. Even if it takes time to get better and delays your academic progress, that's not a major problem. Academia works on very long timescales and several months of low productivity is nothing in the big picture.

At the end of the day, maybe you'll decide you just don't like doing mathematics research. That's okay too, there are lots of other things you can do with your life. Math is particularly difficult in this regard, in that math coursework has a very different flavor from doing research (exercises with short elegant solutions, versus long messy problems with awkward solutions that only accomplish half of what you really want). Liking coursework is not necessarily a good indication of the same for research, so a lot of people do leave the field at this stage. Again, there is nothing wrong with that.

Professional mathematicians tend to be people who really do enjoy doing mathematics research, and they tend to describe the work in terms that make it sound like it is inherently enjoyable and anyone that doesn't like it must be broken somehow. But that's not true. If you get better and discover that you enjoy it, great. If not, that's great too.

Answer 2

I'm not in the business of remote diagnostics, but you sound like you are suffering from (mild) burn-out. You also sound like you are trapped in a vicious circle: setting (momentarily) over-ambitious goals, failing, losing trust in yourself, trying to prove yourself by setting over-ambitious goals -- rinse, leather, repeat.

Break the circle by taking a long vacation and find something that you enjoy. Perhaps other goals outside work, but maybe even better: A real treat that has nothing to do with achievement. Something just for you to feel good. You might want to involve your supervisor to some extent, at least by telling them that you are exhausted and need to take some time off in order to recharge.

But most of all: Seek counsel. Pick up the phone and talk to those old friends. Find out who is in charge of social-psychological counseling at your university (mostly "Sozialpsychologischer Dienst" at German universities) and make an appointment now. You are already in therapy, which is a great, if overdue decision. This will help, but it takes more time than nine weeks to change those harmful cognitive and behavioral patterns that you might have become accustomed to. You need some patience here.

In addition to resolving some more deep-seated issues through therapy, you might want to consider private coaching to address more technical problems. I had good success with a writing coach when I had a bad case of depressing writer's block during the last stage of my PhD.

You might also want to team up with others more often when reading difficult papers. It makes the thinking easier, and it's less lonely. Finally, many papers are just really hard and even bright students need weeks to figure them out. Don't beat yourself up; just try to adjust your expectations. Also in this regard, teaming up with others helps as a reality check.

Related questions:

• How should I deal with discouragement as a graduate student?
• "I've somehow convinced everyone that I'm actually good at this" - how to effectively deal with Imposter Syndrome
• How do you come to terms with the fact that you might never be among the best in your research community?

Answer 3

First of all, you're doing the right thing by reaching out and asking the community for the best way to proceed. There are people out there to help you! Many, many students have gone through similar situations and have found a way out. But first, let me address some of your questions.

Where should I have foreseen my problems?

It sounds like one of the reasons you're struggling is being relatively new to research. Trying to discover something new is very, very different from taking courses, since you're working at the frontier of your discipline. That means it's hard - for everyone. In theory, you could have learned the difficulty of doing research by trying it out earlier (when the thesis wasn't hanging over your head) - but it's definitely not too late to adjust!

Which signs did I ignore? Where did I miss to put things on the right track?

When you're spending weeks of your time feeling that you're not making any progress, it's probably time to talk to your advisor/grad students/someone experienced and ask for their advice. This is far better than struggling on your own and feeling worthless.

How shall I find value in myself, now that I have found myself incapable of pursuing research, and have lost everything else?

Regaining self-confidence is really important. The fact that you've been struggling does not mean you're incapable of doing research. I can think of several reasons why things have not been well, none of which are impossible to overcome:

• You might not have the necessary background

This would explain why reading papers takes so long. Start by identifying general topics discussed/used in the literature you need to understand. It's really hard to understand them from the work itself (I've been there), so I would recommend looking for more general resources like textbooks, online courses, etc. Once you understand the fundamentals, it will be much easier to understand what the authors are trying to do. And no, you weren't necessarily supposed to get it all from your courses, since some of the topics may be specific to your particular area of work.

• This particular area is not your calling

Many scientists change research areas and even disciplines several times before finding the one they like. If you are not excited by your work, that's ok! It might or might not be too late in the year to switch to a different area altogether, but in either case, the fact that this particular line of work has not been successful does not mean others will not be much easier/better suited for your interests.

• The problem you're working on is really hard

Since you're not an experienced researcher who has spent decades in the field, it is expected (by most people, at least) that you cannot just jump in and start cracking complicated math problems people have been working on for years. Maybe your problem is just really difficult! I'd say, at this point the most important thing for you is to finish your degree without completely destroying your nerves and your ability to perform research at any point in the future. That means - pick a problem you can solve! Even if it's really small, this little personal victory might help you remember what it's like to actually solve something. Then, think of the smallest possible set of problems you need to solve in order to put together a thesis. If you can do something other than what you've been doing, that might help. If not, get the background knowledge you need (see the first bullet point), break down your tasks into small parts, and ask for advice if you run into roadblocks!

Most importantly, don't be too hard on yourself. Research is hard, and you've experienced that first hand. And remember, you are not alone. I've found MIT graduate student blog to be very helpful, since oftentimes students share their own struggles - and how they learned to cope. So definitely check it out and best of luck!

Answer 4

I think the first to address are your health issues. Depression makes it really hard to concentrate on work. When I was on antidepressants I remember reading and re-reading papers with no other result than increasing frustration. In my opinion, you shouldn't even work while on antidepressants. It's like trying to run with a sprained ankle confident that it would work since the joint is immobilized.

As others pointed out, your depression could be a consequence of the burnout. Many of us have had the same issues you describe. And we got upset for not making progress, for not having time to go out with friends, etc. The wrong answer to this is to work longer ours and to worry about your fitness for an academic career. Unfortunately, many do just that, and end up either depressed, or they simply leave the academia. And it has very little to do with their actual potential as researchers.

To get things under control, I'd suggest what doctors suggested me to in order to keep my mental illness under control: develop healthy life routines and re-socialize. For example, keep waking up at the same time and try sleeping the same number of hours at night, eat the meals at the same hours, start and finish work at the same hours, and religiously take your medicines. The second part is to set aside time to go out with friends. They have to trust you that on certain days you will always be free to spend time with them. If not, try hanging out with your current colleagues.

You also talk about taking a lot of time to understand papers. In my field, there are two ways to read a paper: a) just get the information on what the paper is about and what new result is reported, b) study the paper carefully, so you can reproduce their result and use the techniques developed there in your own work. Needless to say, b) takes the longest, so a few weeks to a few months is understandable. But, a) can be also frustrating if you are new to a field and you have trouble even with the terminology.

You shouldn't worry if there seem to be gaps in your knowledge. The more you learn, the more you realize that those gaps are infinite abysses. Your job as a researcher is to venture into those abysses and find beautiful and exotic things no one has seen before you. Course work, reading and your own work, only serve to give you some support. Again, it is counterproductive to question your academic ability. It is better to look for ways to improve your efficiency and work quality. And for that, do not hesitate to talk openly to your colleagues and adviser.

Answer 5

It is completely normal to feel stupid when doing research. Often, you cannot see how to solve a problem right away. Sometimes it takes a long time to even figure out what the problem is. This is part of doing research. It is maddening at times. It is depressing at times. You are creating new knowledge and mastering new knowledge on the edge of knowledge advancement.

It is not at all like learning at an undergraduate level, where the answers exist somewhere and have been filtered through textbooks, better explanations, real applications, and analogy.

I recommend this short essay article from the Journal of Cell Science: "The importance of stupidity in scientific research"

I also recommend Barbara Oakley's new MOOC "Mindshift: Break Through Obstacles to Learning and Discover Your Hidden Potential"

Answer 6

I am not in the field of mathematics myself, but as an outsider, I think mathematics is very hard and what you are describing sounds pretty normal for a mathematician. Only I think you set a bar way too high for a master thesis. Five semesters for a masters program sounds pretty hardcore to me. This is not a PhD. Your mindset at this point should be to "get it done!". Focus on getting your diploma as fast as possible and getting it over with. Masters courses are not designed to get students to make scientific discoveries. If you want that, go for a PhD after you get your masters degree.

Also, check if your meds have dizziness, drowsiness, etc. side effects. Those will chemically turn your brain off. I can't do intellectual work even if I take cold meds.

Finally, if you haven't seen it yet, watch A Beautiful Mind (2001). As you do that, remember the main character there is arguably the greatest mathematician ever, he is doing a PhD in a world's top university, and he is still struggling.

Answer 7

TL;DR: Be superficial with papers. Most of them aren't important anyway. Try to catch the broad idea or the reason why you don't need them. Focus on few important ones and don't worry to spend weeks on each of these.
Follow any idea you get. Cut your topic in parts some of which are easy to solve. Discuss the partition with your prof. Don't focus on psychology but on mathematics and some fun.

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@Nate Eldredge said "there is a large gap between what you learn in coursework and what you need for research." I want to deepen this because it might give you some hints where your mathematical thinking might still be too much student-like and too less researcher-like.

As a student, you are focused on achieving your exercises and exams. Both are closely connected to the matter of the respective lecture, so the lecture's content always gives hints on how to solve the tasks: The intended solutions often apply a theorem from the lecture or mimic a proof of such a theorem. There is few incentive to use knowledge from other fields, because such problems would be too hard for students that happen not to have (yet) studied the other field. So "exam knowledge" is often detailed but narrow.

Research questions don't give such hints. In fact, innovative and cool research often consists of applying thoughts from an alien field to an old problem. So for research work, your mathematical knowledge needs to be a broad overview without focusing too much on details. You need to know what is in your mathematical toolbox. You don't need do know how each tool works in detail, since once you find a useful tool-thought, you can and will easily afford some months to work out the details in a rigorous way.

This leads to another important skill for mathematical research. It is that paper reading you are struggling with. You say you take too much time to understand them thoroughly. But this is normal. Therefore, nobody (well, except the peer reviewers, I hope, and the ones who want to improve exactly its result) ever tries to understand a paper thoroughly. Most of the time a superficial understanding is sufficient to know why you don't have to consider a particular paper any more. Find brief words of this superficial understanding for the discussion with your prof and later for your thesis and then move on to the next paper. In the end, there will be only a handful of important papers for your thesis. Once you have them identified, don't worry about some weeks to study each of them thoroughly.

If any paper triggers some --maybe unrelated-- idea to you, feel free to follow this thought for some hours. Make some notes about it, they may come in handy later on. Also this way you exercise getting ideas apart from the guidance of a lecture.

Unfortunately, many professors aren't aware that paper reading is a skill students might need help to get accustomed at. So tell your professor what you understand and what not. What does she think of a paper you both read?

Another important research skill is to cut your overall research topic in separate small chunks and find the specific research question to answer (in this order!). Half of the chunks are ideas you have already in your toolbox, half of them are "real work" you'll solve somehow. Discuss these things with your professor. On some things she'll give you some hints ("I know this is not feasible because...", "yes, this might work with the idea in paper ...") and on some things she'll show you that you aren't that bad as a researcher because she doesn't have a clue as well.

So your questions: "Which signs did I ignore?" -- In one of my final exams, the professor asked me about the broad idea of a theorem without formulas. I knew the mathematical proof but I wasn't able to "proof by picture". This worsened my grade but taught me an important lesson about research thinking I am still thankful for. Maybe you happened to miss something like that.

"Where did I miss to put things on the right track?" -- You did not. It's still the right time to adjust your way of working as mentioned above. Also, reiterating the other's answers take breaks, do some sports, meet friends. This "rearranges" your thoughts. I get many of my ideas cycling in the countryside.

"How shall I find value in myself, now that I have found myself incapable of pursuing research, and have lost everything else?" -- Focus on mathematics, not on your psychological condition or on the treatment. That's the psychologist's job, not yours. If you want to solve a mathematical problem, your sorrows about "value in yourself" is of no concern, it's rather a distraction.

Answer 8

Any or all of the other answers may be correct, but here's one additional idea: You said you are on anti-depressants. This implies that something physiological is messing with your brain. If so, it may also be interfering with your ability to concentrate and reason. Some anti-depressants can also have that effect.

Answer 9

As a current student studying computer science, sometimes when working on bigger and more serious projects, I as well feel like creativity is missing and the knowledge that was lectured by the professors is not enough. The first step to those type of problems (this is entirely in my opinion) is to stop and to acknowledge that what you got is not enough. You will need to dig harder in order to succeed in your projects. On my recent project that took almost 6 months to develop, 2.5 of those months were like a hole. Nothing I was doing was productive but took some time to reflect and plan exactly step-by-step what I needed and I got it done. My advice to you is that you need to plan small steps to achieve the final goal, which in your case is the thesis, and the time where you think you're not productive nor creative don't think it's negative, by the contrary, it's normal.

Answer 10

There are a lot of very good answers here, especially the suggestion to take a break, but I would like to point out one important take away from my personal experience: Return to your motivation. Research in general is not only difficult and frustrating for everyone (even those who put on a good face), but also is constantly evolving be nature, which makes people who are at any given moment not moving forward feel like imposters even though this non-differentiable progress is part of the process. Use the knowledge of this psychological paradox to ease your mind, and then review your motivations.

I also double majored in physics and mathematics, and I earned a masters in computer science afterwards. I then worked for 3 years at an R&D firm and am now back earning my PhD in Robotics. I changed my field a few times, albeit in small moves, because as I reviewed the problems I was taking on I realised that my original perceptions oI can tell you with certainty that through this entire process I have gotten into a rabbit hole with my work more than once, and there are a few solutions, but the most helpful one for me is to return to the original questions. Ask yourself:

• What problem was I originally trying to examine? and why? I know as a masters student you don't often have a lot of say in what you are doing, but you often have more control over how you do it then you think.
• Why was I interested in this, were my original perceptions about what made this problem interesting correct, and what has changed about my understanding of the problem given what I know doesn't work? This question is extremely important because if you return to the original problem with your new-found knowledge you will likely find that, given what you now know, you would have probably taken a different approach.

The answers to these questions will make you feel a lot less "boxed in", and if you end up wanting to continue pursuing this question, it will give you a lot of clarity on your next steps.

To your specific questions:

• Where should I have foreseen my problems? Realistically, you couldn't have. People who have success anticipating and avoiding failure fall squarely into 2 categories: people who are lucky and people who have failed a lot and pulled themselves up. Anyone who seems otherwise is masking the truth, or you don't know their whole story. Remember, all research is like 5% success, 70% failing and moving on, and 25% failing and trying again. You should never feel alone, as you aren't. We researchers are here with you :)
• Which signs did I ignore? In all likelihood, none. I have a huge problem with this aspect of research; that the results are all that is exposed to the outside world, and the process is so separate from everything. I suggest it to everyone, but you have got to read The PhD Grind by Phillip Guo. This guy graduated from MIT with incredible success, went to Stanford for his PhD, and a few months in immediately felt his world collapsing around him. He documents his struggles, his good times and bad, and how he eventually came out after taking the time (much longer than he expected) to figure out what really drove him and how to live his life in spite of feeling like his ideas didn't always pan out. It is what motivated to go back to academia after I left, and could really help (its free, and a very quick read!)
• Where did I miss to put things on the right track? Common misconception: there isn't a right track, it just feels that way because you see other people and think "Thats where I should be. That is right" It isn't (see the first bullet point), it is just there track, and you have yours. Not to get too philosophical, but we are here for a limited time, and there is no knowing how what we do will effect the future. As such, the "right track" for you must be a more holistic gauge; continue trying things, continue caring about yourself and the world around you, do not remain idle, and you will find that you will be able to look back on your "track" proud of the path you took.
• How shall I find value in myself, now that I have found myself incapable of pursuing research, and have lost everything else? Finding value in ones self is a hard pursuit, and do not pay attention to those who trivialize it or propose a quick "silver bullet" answer. I believe firmly, however, that you can find value in action (see above). Pursue life relentlessly, and you will find that the question is not about finding value in general, but finding it in what you do, whether you succeed or otherwise. That might be this research, it might be different research, and it might not be research at all (never forget that there are many companies that would kill for your skill set), but as long as you continue pursuing value and pursuing your path, there is value in the pursuit itself.

I also would like to say that while it may seem as though you have "lost everything else", not only is all that is lost recoverable, but as you are a masters student there is so much more life that you will engage as you continue forward, no matter your field or interests. You say you are a poor student, but objectively you aren't as your studies demonstrate (see above, research is hard!). You say that professors don't want to work with you, but I assure you that professors are very willing to give students a chance with little background (else how did we all get started?! :) ). Lastly, you say that your colleagues are disinterested, but remember what people want from each other: engagement, empathy, sympathy, and support. The minute you stop letting your rabbit hole swallow you whole and you reconsider your motivations, you will find not only clarity in your problem and your path, but you will also find that separating yourself from your work is just as important as doing work. Good luck, and never stop asking for support and help.

Answer 11

I have spent lot of time in research projects. So what you are going through is completely normal. As it is research, you need to go through lot of material, digest them and wrap your head around them and then spend lot of thinking time to apply them to your context. There will be lots of ups and downs, failures, restarts, feelings of inadequacy when you are unable to think through. You need to accept this as part and parcel of doing research.

How I coped with this? When doubts came, I reminded myself that people saw something in me which made them accept me for such work. The more time you spend doubting yourself, the less time you have to think with clarity on your actual work. Secondly, I consumed myself with reading - the more I realized I didn't know, the more I read.The more doubts I had, the more I experimented. That way I found so many ways of not doing something. The process of elimination leads to the right way. There is always light at the end of the tunnel. Thirdly, I spent some time doing what I liked whenever I had any mental block.

Research is overwhelming but as you have been accepted for it, that itself is a great affirmation that you can do it. My advice is avoid the pitfall of negative thinking and promise yourself that you will not waste a single minute entertaining thoughts which are not related to your research.