If you are new to research, of course, your claim doesn't have to challenge the experts, just impress your teacher.
Booth, Colomb and Williams
(The Craft of Research, 3rd ed, p. 126)
In academic writing it is never enough to be right. At our monthly craft seminar, yesterday, Rob Austin put it very nicely: your work needs to be "compelling", and this requires that it be both insightful and convincing. Booth, Colomb, and Williams talk about "making your claim significant" (124-126).
Part of this means being aware of what counts as evidence for a particular group of people. Your research process will have to generate exactly that kind of evidence, and your research writing will have to put it before your reader.
Nicole Berry, an anthropologist now at Simon Fraiser University, apparently held a talk about this issue in 2004.
As I write my dissertation it seems to me that the linguistic data that I have, particularly long transcripts in Kaqchikel Maya, severely restrict my audience, the same way that including lengthy mathematical formulas would repel potential readers.
It is very true that some forms of evidence repel certain audiences. But there are many academic audiences that simply require you to express yourself with mathematical precision, others that require you to quote from your transcripts in the original language. In both cases, you are then normally just as obligated to translate these expressions into prose that can be understood by an ordinary academic reader.
Many members of your audience will take your word for the translations. They will expect both the peer review process and (post-publication) the critical community of your peers to ensure that everything is more or less in order on matters they can't understand. In the long run, the fact that your basic understanding of Kaqchikel Maya (or your math) has not been questioned by those among your peers who are qualified to do so, builds your credibility. It's what makes you an expert.
It is important to make this mental transition to a more general academic audience. At some point (preferably before writing your master's thesis) you have to stop trying only to impress your teacher. Instead, try to be compelling, as Rob says. That means understanding not who exactly you are writing for but what kind of reader you want to convince. Decide on your audience. Then find the relevant evidence.