My advisor wants me to make my PhD thesis weaker 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:


Giving a list of examples of said objects;
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!
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!