Master thesis advisor gave me an ill-defined question. I worked on it for a year!

Question

My master thesis advisor gave me an ill-defined question. His expertise is in mathematical optimization, but he wanted to shift to heuristic optimization so he assigned all his graduate students topics in that field although he actually doesn't know much about it.

He assigned me a problem. I had a feeling that it was ill-defined. I worked on the problem he assigned me for a year but now the numerical results affirms that I was right.

I am not sure how to deal with the situation. Should I waste more time trying to re-formulate the statement of the problem? I feel it's unfair for me to be both the student and the mentor! What is his job, really? If I'm to do everything on my own...

He doesn't know anything about this field he forced his students to work in.

However, if I quit probably no one is going to believe that it is his fault as a mentor and won't find anyone in the department to write me a recommendation letter to start fresh somewhere else.

So, what are my options now?

Is it advisable to tell the truth to other professors? Will they believe me?

Answer 1

I think this question has already been given a perfect answer.

But I would like to add something that I think might be highly important in your specific case:

Do not trust numerical results.

Before saying to your advisor that he is wrong, or even worse, trying to alert other people of this, make really really sure that you can trust the simulation results.
And then don't trust them :)

If you have a formal proof of something that's great. If you have a numerical simulation that supports your point of view, it's highly doubtworthy. I've often seen small changes in parameters or a tiny bug in the code completely change results.

Even if your code is flawless, other people will probably not believe that. There's a huge replication crisis in computer science, numerical results can often not be replicated.
Unless your code has been peer reviewed and ideally re-implemented by another team, people will assign very low credibility to your results.

I would advise to report this as neutral as possible. Make a really clear definition of the question that was originally stated. Explain your simulation in detail. Provide results.

Answer 2

You (and some of the commenters) have a misconception about mathematics, and even research in general. You need to dispel that and present what you have done and learned in a way that satisfies your advisor so that you can finish your degree.

Comments about research in general

If your advisor knew the answer before giving you the problem, then it wouldn't be research. Research is an exploration of the unknown. All research questions are "ill formed" at the start. People notice an anomaly or a missing piece of theory and ask "What in the world is going on here?". There are not immediate answers. Einstein said “If we knew what it was we were doing, it would not be called research, would it?”.

Since you are exploring the unknown the results could come out to be anything at all. You start with an idea that "might be true". If you set out to "prove that it is true" then you are doing propaganda and not research. You want to take the attitude that "How do I show whether this is true or not?". Starting with preconceptions can easily lead you astray into scientific misconduct. Reality is brutal.

And no, in doctoral research you don't need "positive" results. You need to discover the truth. Learning and establishing that some hypothesis is false is just as valuable as knowledge as knowing that it is true.

Comments about mathematics in particular

Mathematical research shares a lot with research in general. It is a search into the unknown to find truth. But establishing that, for example, Fermat's Last Theorem was false would be precisely as valuable as showing that it is true. Possibly even more so, if it led to new insights. But it is what it is, not what you want it to be.

And, again, if your advisor knew the answer to the question posed to you, then you wouldn't be doing research but only, perhaps, confirming something already known.

What to do

You actually have written your solution within your question. You say "I worked on the problem he assigned me for a year now but now the numerical results affirms that I was right". That is a result. It is precisely what mathematics is about. Write that up. You have been successful at doing mathematics. You haven't failed. You have succeeded. You have insight into a problem. Perhaps you have insight that no one else in the world has at the moment.

Answer 3

Lots of people are trying to tell you about negative vs positive results, but they might be a bit wide of the mark - it sounds like you see your difficulty as having an ill-defined problem statement, not a negative result for a well-defined problem statement.

Previous answers are correct that "X is false" is a perfectly good result, even if you were hoping that X might be true. However, "X isn't a properly defined problem" isn't a publishable result, so I understand your concern.

You have shown something numerically. Could what you have shown be formed into a suitable problem statement? It's difficult to comment without knowing any details, but if e.g. you were given the problem "solve optimization problem X", and you subsequently discovered problem X doesn't admit a unique solution, you could pose a question "Do optimization problems of type X always admit a unique solution", for which you have found a perfectly good (negative) answer. Your advisor should be able to assist you with such a re-framing, even if he's not as familiar as he should be with the details of the new field.

Finally, as WoJ is saying, don't lose too much sleep if your Master's thesis isn't the greatest piece of research ever. A Master's is a baby PhD, no-one's Master's is all that good. If you're capable of anything beyond simply following your advisor's instructions, you're doing better than most Master's students. Keep on your advisor's good side, don't make a fuss with other professors, and just quietly go to a different advisor/institution for your PhD, that's my advice.

Answer 4

In my opinion, a student needs guidance, especially for a Master thesis or at the beginning of a PhD.

I know very well what it is like when your advisor just gives you a general idea what to research, but does not really answer your questions or read the material you have already written. So I understand that the OP suffers.

If the advisor gives you a problem, but doesn't know the research area well, it is quite possible that the problem is either trivial or much too hard, and the advisor cannot guide you on the way.

So while some people might think it is good to just throw the student into the ocean and tell them to figure out "swimming" themselves, I consider it bad practise.

So what does that mean for the concrete problem of the OP? Learn to swim, even if it is an awful kind of swimming. Write up what you have, show what you have done and what you found out. It may not be great, but don't spend another year on polishing it.

Answer 5

You did not mention your country but at least if you are in Europe the contents your Master thesis do not matter. The Master degree does, of course, but nobody cares about what is in the thesis if it remotely makes sense.

Have a chat with your advisor and turn it into a "I proved that X and Y do not work". It is perfectly fine.

Have a quick look at other master theses in your department and give one or two a closer read. You will see 50% of introduction, 40% of graphs (big graphs), 5% of acknowledgements and 5% of actual findings (if any of substantial nature).

This is absolutely normal - we are talking about a Masters, something zillions of people get and one cannot expect each of them to be a breakthrough and reveal a new scientist every time.