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I am currently writing my master thesis in mathematics and for those who are more familiar with the subject, I am more into analysis whereas my supervisor is more into computational sciences. My project is on an application of analysis and there is also a numerical component.

I will soon submit my first draft to my supervisor but I am slightly anxious about how he will react.

To describe it quite generally: my background is very much in the theory of mathematics and I am a relative novice in the computational sciences, thus I am treating that component as an end-goal of my thesis while building up to it rigorously with the theory that I have become acquainted with over the years. Incidentally, in our meetings, my supervisor focuses most of his attention on the "results" of my thesis rather than the technicalities in between.

You could argue that there is a "mismatch" in some sense. However, I am very much interested in this application which my supervisor does, but I would like to do it in my own style. This brings me to my question: do I have to write my thesis in such a way that he is able to read it, or is it quite common for them to seek the assistance of other professors who are better acquainted with the theory?

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    You need to write your thesis so that others in the general field can understand it. This includes your advisor, the professor next door, and bonus points if you parents can at least get most of the way through it with some idea of what is going on. – Jon Custer May 30 '17 at 13:23
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    By the way - writing is hard. Writing clearly is harder. Your first draft will be neither clear nor particularly well written (opinion based solely on personal experiences dealing with students). – Jon Custer May 30 '17 at 13:25
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    @Jon Custer Why should other mathematicians understand it by default? – Marko Karbevski May 30 '17 at 16:09
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    @JonCuster I have a friend who is writing his master thesis in category theory. I, for the life of me, cannot follow it. I also think that mathematics is incredibly broad and diverse and many branches are completely unintelligible to me. – Jason Born May 30 '17 at 16:15
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    The burden lies directly on the writer is to make the article/thesis intelligible to the intended audience. Sure, the audience may have to delve in to the references, work their way through this equation and the other, and what-not, but it has to be a clear exposition of the problem and the path through the solution. If your supervisor can not get the gist of it, then you should not pass, since you have not laid it out so they can distinguish brilliant math from hopeless fluff. – Jon Custer May 30 '17 at 16:23
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YES most definitely. Obviously, if you supervisor cannot comprehend your project, they cannot supervise it.

This should only very rarely occur. I can only think of a situation in which the student has, from prior qualifications, superior knowledge about certain aspects of the project than their supervisor. In this case, perhaps supervision in the traditional sense is not really necessary, but merely some guidance and feedback.

In any case, if you want to publish your research in the field of your supervisor, then you should speak a language and use conventions that people like your supervisor can comprehend. If you cannot express your project in such a way, then how can you hope that anybody relevant can understand it?

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If you write a thesis in a way that even your supervisor cannot understand it, then you have found the wrong level of abstraction.

In general, write a thesis at a level so that a second year graduate student -- i.e., who you were when you started this research -- can understand it. I would imagine that it is a reasonable assumption that every professor in a department is able to understand any second year graduate student material, even if it is maybe not in their immediate field of research.

Of course, a general truism in almost anything related to academia is that that is a question you ought to discuss with your supervisor!

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Mathematics is one of the fields where writing theses and papers that only the topic experts can understand is accepted. Some areas would not be able to make progress otherwise.

However, you chose to write with someone who is not method expert, but rather comes from a different field in which you locate your applications. In other words, you ended up writing an interdisciplinary thesis (whether or not your methods are interdisciplinary is not relevant, rather the fact that you chose to pick a field which bridges two areas).

This means that you have the double trouble of making sure that your methods are fine and applicable, and that you now have to communicate to two communities. One of them is represented by your supervisor. This means that, yes, he should be able to follow your work at a reasonable level of detail.

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This is a tough one. You may want to wait to unveil the theoretical underpinnings section of your draft for the time being -- you could say that you want to work on that section some more before sharing it with him -- and give him the results section first.

In the meantime, I suggest you look around for a co-advisor who will be able to understand the theory section.

Otherwise, if you try to write the theoretical section in such a way that you include a primer for all your ideas, such that your advisor can really understand and appreciate them, you might end up with the equivalent of a textbook or two weighing down the first part of your thesis.

But I don't have a crystal ball. It's possible your advisor will be happy with a strong results section, and just let you write what you want in the theoretical section.

[Worst case scenario: you don't find an appropriate co-advisor, or your advisor doesn't accept the idea of a co-advisor, and your advisor wants you to exclude the theoretical section. If that happens, it's probably not worth a big fight. It would not be the end of the world for that section to go on a back burner for now, to be incorporated into another project farther down the road (perhaps in a PhD thesis).]

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