My advisor wants me to make my PhD thesis weaker

Question

I am a final year PhD student in mathematics at a university in Spain and about to submit my thesis in a few weeks. During the last months, I have been writing up the remaining details of a project. Let me make clear that this project is not the only one contained in my thesis. However, it is the heart of the thesis and the other projects contained in my thesis, while in some way independent, yield interesting results when combined with the project I am talking about in this question. Moreover, the topic of the project was proposed by my advisor, but I mostly worked on it without talking to him (he was visiting other universities and sick for a very long time, and there were other reasons as well).

The project is a classification of certain objects, meaning that it consists of two parts:

1. Giving a list of examples of said objects;

2. Showing that the above list is in fact complete.

While coming up with the examples was kind of hard at the beginning, it was pretty straightforward and algorithmic once I got the hang of it (I always told my colleagues that one could teach a chimpanzee how to do it). The mathematically involved and complicated part is to show that the produced list is in fact complete. This involves several creative ideas and is highly non-trivial.

My advisor now thinks that the thesis is too long (it is about 130 pages, part 2 being roughly 25 pages long), and that I should remove part 2 from the thesis (i.e., that I should not show in the thesis that the list is complete): according to him, a longer thesis has more potential of containing small, subtle mistakes, and obviously mistakes are bad. He said that he cannot be sure that everything is correct, since he never read all details and I need to submit rather soon. He is also travelling and busy until I am supposed to submit.

However, I do not want to cut the second part of the thesis, for the following reasons:

• I already have the proof, and I am sure that it is correct. Why should it not be included in my thesis? The alternative is to include an unproven claim in the thesis, similar to "the list is in fact complete, which we will show in a forthcoming paper".
• If I remove it and only keep part 1, my results are incomplete and the project only consists of "describing some examples", which is - as I explained above - pretty easy once one knows how to.
• Obviously, I want my thesis to be as strong as possible.
• The interplay between all projects of my thesis cannot be made as strong, as well.
• I know who the referees of my thesis are going to be, and one of them is notorious for being a very harsh grader. While I am pretty proud of my thesis in the current form, I am afraid that removing part 2 will affect the grading of my thesis.

I explained my point of view to my advisor, but he kept saying that the thesis is too long (apparently the period of time the referees are given to evaluate the thesis is pretty short) and that it is too unsafe for him to submit it as in its current form.

How should I behave in this situation? I am extremely thankful for any advice!

Answer 1

If it isn't going to damage the relationship with your advisor too much, you should submit your complete thesis. The arguments you provided from your advisor are pretty weak, and I'm quite sure that 130 pages isn't particularly long. Your arguments to keeping the length are compelling (strength of ideas, likelihood of appeasing difficult thesis committee member, etc). That said, we are only hearing your advisor's opinion second-hand. It's possible you are not giving us all the information, either because you misunderstand your advisor or your advisor has not fully detailed his concerns (which is definitely not optimal).

You said you mostly worked on this without talking to him. I may have missed it, but I don't see that you have explained your reasons to your advisor. Is there time to do this? Ask him what would happen and how would he feel if you submitted your thesis as is? This should preferably be done in person, but you may need to phone or email him.

Good luck! Thesis time is always stressful, even under the best of conditions!

Answer 2

The main thing to keep in mind is to finish your degree. If your advisor thinks that leaving that part out helps in that goal then you should consider it. It may be that a minimal but sufficient dissertation is advantageous here.

However, that doesn't mean that you abandon the work. You have, in fact, the basis for an additional paper that can probably be published separately from your dissertation, giving your early career a boost. Expanding the work of your dissertation is a pretty good way to get started in academia.

Think about the short term (getting done) and the long term (building a CV). A long thesis might be good or bad, but an extra paper is good.

Explore it with your advisor. I'm assuming, of course, that he is experienced and well aware of the system you are in and the likely outcomes.

Answer 3

I think the "length" argument is a red herring and I think it's influencing your thinking too much.

I think it's more likely that your advisor is simply not comfortable with the second part of your thesis. I suspect that the uncertainty that your second part is correct may actually be a feeling that your second part is wrong or incomplete (perhaps because of the "creative ideas"), but your advisor has not yet been able to show definitively that it is wrong. He's likely concerned both with his own reputation among his peers and for the success of your defense if your reviewers are similarly unconvinced.

If you are certain that your proof is correct, then it's up to you to convince your advisor of this. If you can't convince your advisor, your chance of convincing your committee is slim. It seems that the time it will take to convince your advisor is longer than the time between now and when you will defend. In that case, your advisor's suggestion to leave the second part out (especially if they feel the first part is sufficient to support you passing your defense) is quite reasonable. You mention that there are other aspects to your thesis, as well, so this means excluding only one (potentially problematic) part of one project of multiple that make up the whole thesis.

It doesn't mean that you abandon the second part of this project, only that you exclude it from your thesis.

Answer 4

Two reasonable goals at this point are

1. graduating with your Ph.D. and
2. publishing your mathematical discovery.

As other answers suggest, achieving the second of these goals is possible with or without including all your current results in your thesis. Thus my general advice is to focus on the first goal.

As members of the community at large, there is no way we can possibly guess at the behind the scenes politics that goes into awarding PhDs at your institution, particularly when you have a particular committee member who's rumored to be a "harsh grader" and an adviser giving unusual advice. What we can affirm is that your adviser is giving you some unusual advice about a thesis that is not that long (even in math, where the PhDs tend to be shorter than in other fields). He may have good reason for it, or he may not, and as a student it will be hard for you to judge. I'd strongly recommend repeating your question to your graduate chair and a second member of the thesis committee you trust and asking for their independent advice before making a final decision. It appears you could use an advocate in this situation, and it's unclear whether or not your adviser is acting as such.

Answer 5

If I remove it and only keep part 1, my results are incomplete and the project only consists of "describing some examples", which is - as I explained above - pretty easy once one knows how to.

Since you are saying that the first part is the easier one, I would suggest cutting that one shorter instead of the second part. Whether you cut 25 pages of the second part or 25 pages of the first part shouldn't ultimately make much of a difference to your advisor if he is really just worried about the length.

Additionally, you could try to find some compromise of cutting it by 15 or 20 pages instead (or whatever you think is doable without ruining your thesis) if you don't want to cut that many pages from the first part either. In my experience compromises usually work better than a straight out "No".

Answer 6

You could move part two into a appendix. That could be a compromise which could be acceptable for both your advisor and for you. You can argue that the actual thesis is now ~25 pages shorter and he does not need to read the appendix. You can refer to your appendix from your main text and keep your thesis strong. Moving technical details to an appendix is common. Whether your part two is really technical might be debatable, but could help you to get what you want.

I know of many theses that were initially too long where the author resorted to the appendix way to satisfy formal length considerations.

Answer 7

The problem with a proof that contains "creative and non-trivial" ideas is that one mistake near the start may invalidate the entire argument, and if someone produces a counter-example, then obviously the proof can never be fixed up.

From your description it's not obvious whether it matters from a practical point of view if the classification is complete (whatever "complete" means).

If you have created an effective algorithm which does something useful, maybe trying to prove that it is "perfect" is being too ambitious. There are plenty of useful algorithms (for example to solve NP-complete problems) which are certainly not "complete" - but discovering them and implementing them efficiently was probably worth a PhD.

Answer 8

I stumbled upon your question as I experienced a similar situation back in 1999.

A thesis is a wonderful experience and a once in a lifetime project. Breathe it and Own it. Your supervisor remains a supervisor and you have the right to diplomatically tell him what your conclusions are on the structure and logic of your thesis, rather than he tells you what should be in.

I made my thesis in theoretical quantum physics and the goal was somewhat similar to yours. I had to work on examples and see if a set of equations reproduces astrophysical observation. The thesis was meant to be mainly numerical simulations. However, from literally day one, I disagreed with the derivations of the key equations I was asked to simulate. While he agreed the derivation of the current equations was not so rigorous, he considered that ultimately they should be correct.

The reason he did not want to dwell too much on the foundations of the theory was, first, because there was already a lot of numerical simulations to do for collaborators to model stellar atmospheres and, second, because dogmas exist in science. Break them, and people will appreciate even if your are wrong ultimately. We set up a meeting and derived the equations again. These equations were derived in 1970 by a known astrophysicist who was very knowledgeable in his field but who was not a theoretical physicist. He took as a starting point an equation picked up from A. Sommerfeld in one of his 1930 book Atombau und Spektrallinien, but Sommerfeld made an assumption which was not realistic in our scenario.

During the first year of my thesis I worked on the derivation of such equations from the ground up using quantum electrodynamics combined with Boltzmann type master equations, came up with alternative equations and showed them to my supervisor. He never really read them, too long, dogmas or whatever. I carried on with numerical simulations based on the old and -to me- wrong formulas because there was a demand for this.

As my thesis came to an end, your dilemma came up. I came with a structure, where Chapter 1 would be an introduction, Chapter 2 would be questioning the current equations and deriving them anew, where my equations would popup with orders of magnitudes of the terms I found out to show their importance. And the rest of the thesis would focus on the numerical equations of the old equations. As he read through my proposed outline, he told me to skip Chapter 2. I went home and talked to my girlfriend.

She said, and I tell you the same, this is your thesis, you believe in it, you do it.

Luckily, my thesis supervisor who was nevertheless a scientist seeking the truth eventually read my chapter and agreed that there was something going on, but to him it required more work (we were at 2 months before submission). He agreed I could include it the day after. I included them at the expense of shortening the rest of the thesis. I submitted my thesis and received feedback, defended it and got it hands up. No one can bother you because you know your thesis more than anyone else.

Coming to your situation, I believe that you do not have a publication in a refereed journal of the proof of your completeness. If that is the case, I would, as you suggest, dedicate a chapter on the proof of the completeness. Completeness of something is an important part of mathematical reasoning and characterizes you more than an enumeration of examples. Don't be shy but you can be diplomatic by saying at the end of the chapter that "While we believe this proof is solid, further investigations should be made prior to its publication in a refereed journal". That formulation is to be discussed with your supervisor as it will depend on who will be your referees and the philosophy of your research community.

Regarding your referees, don't be afraid about those who have a reputation of being harsh. Often those people appreciate those who stand up, politely but stand up.

In what this can help you? First your supervisor can remain a good friend of yours in the future as it happened with me. Second, as it also happened to me, in your life as a researcher that Chapter can help you a lot in getting jobs in other disciplines because employers appreciate the fact that you question things and stand up on your arguments more than enumerating.

Answer 9

Octopus' advice is solid, so I would only add a few things. This reminds me of my dissertation defense experience as well: some advice I received was good, some was bad, but all of it was important to consider.

Feedback from your adviser on your work can help with aspects such as style, correctness, or direction. However, the level of rigor in your work says something about the kind of academic you are. Despite some of the comments above, people do read theses and dissertations. In fact, you should be mindful that it will be only a quick Google search away for anyone in the world to access. Ultimately, you are the author, so unless you are 100% comfortable with it, I would not recommend submitting yet.

If possible, try to postpone your defense. I say this for two reasons. First, and perhaps most importantly, you need your adviser on your side. You only have one PhD adviser, and they can help to make or break your career. He/she claims there is not enough time, so provide more time. Second, this will give you some time to submit a paper or two to academic journals. Committees like seeing that your work has already been peer-reviewed and published. It means they don't have to work as hard and are not signing off on anything risky. Plus, publications can help your career immensely.

Of course, if you do not have the luxury of postponing (entirely possible) or you are just in it for the degree (which seems unlikely to me), I would agree with some of the others who suggest compromising by thinning it out elsewhere, and keeping the content which is most important to you. Whatever you choose to do, though, make sure your adviser is on board.

Answer 10

I have two suggestions:

• Ask your colleagues whether they are willing to check your proofs that your advisor has no time to check (and include them in the acknowledgements). This way, not only can you be more sure that they are correct, you can also let your advisor know so that he does not feel as uncomfortable with you putting the proofs in.

• Give one or more talks in your department about your results, including sufficient technical detail so that others familiar with your research area can grasp your precise claims and understand the rough outline of your proofs. When asked any question, make sure you give complete answers. In some cases, when presenting (or preparing the presentation) you will find subtle issues with your original arguments, and can fix it before submitting your actual thesis.

Answer 11

I don't envy you your situation as regards the difference of opinion between you and your adviser. Nevertheless, it's never a bad problem to have more good material than you need, rather than less. So, well done for overperforming :)

Despite being a thesis adviser myself, I don't think I can really tell you the best course of action. For one thing I don't know all the practical contraints that apply, neither the stance of the other people involved. More fundamentally the "best" course is to a large extent dependent on what you regard as most important you.

If the overriding goal is to achieve your PhD then the most pragmatic course would perhaps to be guided by your adviser, whether his advice is optimal or not. As pointed out by others, omitting the completeness part so does not preclude making it part of further work. There may even be some benefit in doing so, perhaps there are some interesting questions that would repay time spent on a later study?

But I can understand your emotional attachment to your thesis, and in wanting to make it as good a work as possible, something part of yourself as a scientist. You might feel that is the most important. If you decide to include part 2 thenyou have to be prepared to defend it in response to questions, and you may have to do that without much support from your adviser.

In any case, I hope you are successful with your PhD, and that you and your adviser reach an understanding. That last might be the most important!

Answer 12

I believe you should submit your thesis in it's entirety. Your advisor is just pushing you to publish both parts and also testing you as to which you will take: easier route (only part 1) which has less chance of having mistakes since it's 25pg less. i.e. less room for mistakes or your true work which is both parts. Go with your head not your gut as a thesis takes brains not luck.