Math Thesis Plagiarism Determination I am an undergraduate student who is submitting my thesis for committee review. However, one of the committee member is unsatisfied and thinks that I attempted plagiarism from my advisor's paper. However, in my situation:

I am writing a result in extension to my advisor's paper;
I have proved new results in the almost exact same setup as the reference;
Since it is my first paper, a great deal of my explanation and logic is inherited from my advisor and his paper. Therefore, a lot of explanation and formula takes the same form (with possible slightly different definition of variables).
I pointed out directly that how this paper is related to previous work and added reference for directly quoted prop/defn.

This committee member will not support my submission of thesis unless I rewrite everything in my own words. However, I doubt if I can rewrite everything instead of simply rephrasing due to the nature of this work. I wonder what are your guys opinion and how I should deal with it?
I wonder whether the committee member is not so much concerned about plagiarism per se as whether you actually understand your advisor's work.  An undergraduate thesis is supposed to involve, at least in part, the student gaining a certain level of mastery of prior literature (as well as building on it.)  This sort of understanding is usually conveyed in a &quot;theory&quot; or &quot;background&quot; section near the beginning of the thesis.
If this section reads like it was copied-and-pasted from your advisor's previous work, then the committee member may be concerned that you don't really understand what you've written and are simply parroting it without any real comprehension.  They may then have doubts that you haven't really engaged with the material in a manner that is really worthy of whatever level of distinction is associated with a &quot;thesis&quot; at your institution.  Being a mathematician is not just about finding some interesting results;  it's also about understanding about how they fit into the broader picture of mathematics, and about being able to convey your understanding successfully to others.   Your institution may value these latter parts just as much as the ability to find new results (and I applaud them if they do.)
If this is the case, you may just need to bite the bullet and rewrite the section.  It's probably OK if the equations remain in the same form;  but the &quot;connective tissue&quot; between the needs to show, in your own words, that you actually understand how you get from equation (1) to equation (2) to equation (3).  (One of the things I always try to convey to my physics undergraduates is that the &quot;connective tissue&quot; between equations is just as important for conveying meaning and understanding as the equations themselves—if not more important.)