The following examples might help you to see how you could analyse the use of personal pronouns in scholarly writing in your discipline to see how and where their use might be acceptable, and shows how they can be removed if desired.

Example Comment Rewritten without a personal pronoun 
Prefacing a statement of the author's argument (e.g. thesis) It is not always possible to prove something; in many cases all one can do is show that certain evidence supports a certain point of view or conclusion.  
a. "The central theme presented in this book is that many of the misunderstandings about the nature of science might be corrected once it is realized just how 'unnatural' science is. I will argue that science involves a special mode of thought and is unnatural for two main reasons, which are developed in Chapter I." (p. xi) In some research, one must rely on circumstantial or indirect evidence which is open to interpretation. In such cases, one can only present arguments, not necessarily "prove" anything, but like in a court of law, to convince the jury, one must explain why it is believed the evidence suggests a certain conclusion be drawn.
Equivalent to: "Jones (2005) has argued that ..."
"... It will be argued that science ..."
b. "I do not wish to argue that people have no responsibility for their health. On the contrary, there is overwhelming evidence that ...." (p. 1572) Clarifying what the author is trying to argue, so use of a personal pronoun is appropriate. Evidence in support of the argument is presented to lend objectivity to the argument. "It is not being argued here that people have ..."
c. "We believe that simple stereotyping of international students as a homogeneous group of ‘Asian international students' or ‘Chinese learners' is not helpful in facilitating ..." (reasons for belief given) (p. 7) Again, "we" used to introduce an argument put forward by the authors. "It is believed that simple stereotyping ..." does NOT work as it is ambiguous as to whose belief is being referred to.
"Given X, it seems reasonable to assume that simple stereotyping ..."
Prefacing a subjective choice by the author The coining of new phrases and terms helps authors efficiently refer to a concept. While there might be good reasons for the author's choice, there is a certain amount of subjectivity involved.*  
c. "As a way of distinguishing these three areas, I will refer to the first as Piagetian approaches to student conceptions, the second as ...." (p. 5) When introducing new concepts, writers often invent some new jargon to make referring to the concept efficient. Since the invention of some new jargon is a personal choice made by the writer, even though they presumably have logical reasons for making that choice, the use of a personal pronoun to describe that choice is appropriate. "As a way of distinguishing these three areas, the first will be referred to as ..."
d. "The name I suggest for the material that accumulates on the surface is 'smust', a contraction of 'smog + dust'." As per (c), but putting "suggest" in lends a certain humility in making the suggestion. "A possible name for the material ..."
Describing what was done or found or what will be done (a "narrative" structure: the writer takes the reader through their "research journey") As the "doing" and the "finding" was done and found by the author(s), it is entirely natural and logical to use a personal pronoun to describe this.  
f. "We assembled the sequence reads with ..."
"We failed to find any clear case of genes characteristic of the algal lineage ..."
"... we observed that ..."
The authors here are taking a narrative approach to their writing; they are reporting on what they did and what they found. Since they are simply accurately describing what happened, this is not subjective writing. "The sequence reads were assembled with ..."
"No clear case of genes characteristic of the algal lineage was found."
g. "We show here that this Tibetan reservoir of elastic strain energy is drained in proportion to ..."
"In Supplementary Information we present additional GPS data from ..."
"We attempted initially to emulate the observed velocity field ..."
"Our study indicates that ..."
"We assume that frictionless aseismic slip occurs ..."
"Although we tested several different northern boundaries for the model, we ultimately selected a northernmost ..."
Similar to (f), with the addition that the first two examples refer to what the authors are doing in the paper rather than what they did during their research.

Note also in the alternative versions, that removing the personal pronouns forces the verbs (the doing words) to the end of the clause or sentence, which might make things harder for the reader to follow as they have to wait to find out what the "action" is.

"It is shown here that ..."
"In ..., additional GPS data from ... is presented."
"This study indicates ..."
"For this work, it has been assumed that frictionless aseismic slip occurs ..."
"Although several different northern boundaries for the model were tested, a northernmost ... was ultimately selected.
"... I will address this question in section 4."   "... This question will be addressed in section 4."
Using "we" in single author papers 1: Taking the reader on a journey Perhaps more commonly used in theoretical papers or theoretical sections of papers. Also can have the connotation of "you the reader and we the authors" in multiple author papers.  
"We [meaning you and I] can get into Southbank by catching a CitCat from UQ." Not a scholarly example, but used here to demonstrate an occasion in everyday life where an individual, perhaps someone hosting an interstate visitor, would use "we" rather than "I".  
"We can see from Fig 1 that the effect of doing X was Y." Do you find one form of writing more engaging than the other? "From Fig. 1 it can be seen that the effect of doing X was Y."
"We can simplify this expression by noting that |x/a| << 1."

"We can see what this expression means physically by ..."

"We've seen above how X influences Y, now we'll look at how X influences Z."

Question: Is the writing on the left more engaging than the writing on the right? "This expression can be simplified by noting that |x/a| << 1."
"The physical meaning of this expression can be seen by ..."
"The influence of X on Y was investigated above, now the influence of X on Z will be discussed."
Using "we" in single author papers 2: Referring to what the community of scholars in a field has achieved or does Experts who have contributed significantly to the development of a field sometimes use "we" to refer to the collective achievements of the community of scholars in a field. Often seen in popularisations by these experts.  
h. "We consider that our equations can be transformed in ways that could, in principle, change them-and then we demand that they don't in fact change." (p. 61)
"One answer is that it is a mathematical consequence of equations-the equations of QCD-that we have many other ways of checking." (p. 92)
"For the next-best-understood condensate, we have circumstantial evidence that it exists, but only guesses about what it's made up of." (p. 94)
  "It is considered that the equations can be transformed in ways that could, in principle, change them-and then it is demanded that they don't in fact change."


a. Wolpert, L. (1991), The Unnatural Nature of Science (Cambridge, Mass.: Harvard University Press).
b. Angell, M. (1985), "Disease as a Reflection of the Psyche," The New England Journal of Medicine, vol. 312, no. 24, pp. 1570-1572.
c. Zhang, C. Silltoe, J. and Webb, J. (1999). Valuing cultural diversity in student learning: the academic adjustment experiences of international Chinese students. In HERDSA Conference Proceedings. 1-11.
d. Confrey, J. (1990). "A review of the research on student conceptions in mathematics, science and programming." In C. B. Cazden (Ed.), Review of Research in Education vol. 16, pp. 1-56.
e. Hunten, D. M. (2006), The sequestration of ethane on Titan in smog particles," Nature 443, 669-670.
f. Aury, J. M. et al (2006), Global trends of whole-genome duplications revealed by the ciliate Paramecium tetraurelia," Nature 444, 171-178.
g. Feldl, N. & Bilham, R. (2006), Great Himalayan earthquakes and the Tibetan plateau," Nature 444, 165-170.
h. Wilczek, F. (2008), The lightness of being: Mass, ether, and the unification of forces, New York: Basic Books.

* A striking example of this in particle physics is the naming of the particles which make up protons and neutrons, namely "quarks", after something in a line in the book Finnegans Wake by James Joyce.