In what tense (present/past) should papers be written?

The rules of thumb are:

• Established facts are reported in the present tense (“The path of light follows Fermat's principle of least time”). However, you should use the past tense when you refer to previous work in the field (“Maxwell et al. demonstrated clearly in a laser cavity experiment that no mirror is perfect”).
• The experiments, simulations or calculations you performed are narrated in the past tense (“We dissolved the remaining solid in a 5:1 solution of acetone and benzonitrile, and heated to 200°C for three hours.”)
• Discussion of the data presented in the paper uses the present tense (“The results obtained, shown in Fig. 3, clearly emphasize that the cell colonies grew faster on pink toothbrushes than green ones. We attribute this to the color-sensitivity, or kawai factor.”)
• Mathematical proofs are written using the present tense, because going through the proof occurs at the time of reading (“From Eqn. 1, we derive the following system of inequalities”).

Overall, the choice of tenses is actually pretty logical.

There are two distinct general cases that bring up the question of, "Which tense should I use?", each of which follows different principles.

First, are you describing research itself and ideas from research? (This is what you are doing probably 99% of the time.) In this case, the principle that I follow is simple, regardless of whether I am describing what other people have done or describing my own work:

• Historical occurrences should be in past tense. "Historical" means anything that actually happened in the past, whether a procedure, an article publication, a statement made by anyone, or anything else that has actually happened.
• Enduring truths should be in present tense. "Enduring truth" in this context only means that the authors present such statements as ongoing facts in the past, present and future; it doesn't mean anything more than that. (In particular, even if you disagree with what some authors consider to be true, it is still an "enduring truth" in their minds, and so should be presented in present tense.)

The second case where tense is involved is trickier: are you describing your own writing process as you are writing the article? (Although you only do this 1% or less of the time, it leads to perhaps 80% of the confusion of the question as to which tense to use, so it is important to understand this.) The basic idea here is to anticipate your reader's expected or intended path of reading, which is what makes it so tricky. Here is the principle I follow here:

• When describing anything you write in the current paragraph or any paragraph below, use present tense. Future tense could also be correctly used for most things in paragraphs below, but not always. In particular, when referring to elements outside the main body of the text (such as appendices, references, footnotes, acknowledgements, etc.), you should always use present tense, since the reader should refer to such ancilliary sections simultaneously with reading the text. I find this a bit confusing, so it is simpler for me to only use present tense and never use future tense, which is perfectly acceptable.
• When describing any thing you write in preceding paragraphs, use past tense. The only exception is that when writing in appendices, you should refer to the main body of the text in present tense. (Technically, you should probably also use present tense if referring to the main body in other ancillary sections [references, footnotes, acknowledgements, etc.], but I never need to refer to the main body of the text in such sections.)

I now follow with several annotated examples to illustrate these points. Some of them are straightforward applications of the principles I have summarized above, though some could be argued as either present or past tense.

Literature review

AuthorA and AuthorB (Year) studied an interesting topic. They applied a cool methodology and found that certain surprising outcomes are what actually happen.

Comments:

• "AuthorA and AuthorB (Year) studied an interesting topic": The study occurred in the past, and so is in past tense.
• "They applied a cool methodology": The authors actually did some analysis in the past, and so it is in past tense.
• "and found that": The authors arrived at their results at a certain point in time in the past, when they made their conclusions; this is thus in past tense.
• "certain surprising outcomes are what actually happen": The authors concluded that their findings not only applied to their study, but indicate some general truths that would continue to apply in the future. Thus, as a description of ongoing reality, it is in present tense.

Methodology Section of My Own Article

We gathered and analyzed certain pertinent data in various stages. First, we conducted an extensive survey. The respondents of the survey reported that they only partially agreed with most of the statements in the survey instrument. Second, we interviewed other relevant respondents. The interviewees enlightened us as to some of the responses on the prior survey. Third, we collected biometric data from the brain electrodes attached to the interviewees during the interviews, which was generally consistent with what they were actually saying (except for some notable discrepancies, which we discuss in more detail below). Finally, we applied some cutting-edge combined quantitative-qualitative analyses to bring everything together and make sense of it all.

Comments:

• "We gathered and analyzed", "we conducted", "we interviewed", "we collected", "we applied": Statements of research methods or procedures that we actually did are past events; hence, they are in past tense.
• "The respondents of the survey reported", "The interviewees enlightened us", "biometric data ... was generally consistent with": Responses and results (whether by people, animals, plants, or inanimate objects) are reports of historical facts: they actually happened in the past. Thus, they should be in past tense.
• "The respondents of the survey ... only partially agreed with most of the statements in the survey instrument", "what they were actually saying": These are tricky. But even when you are reporting what people said to be enduringly true about themselves, their saying such things is a past historical statement. That is, if you were to ask them again today, they might have changed their minds. You can only report what they said as a statement made in the past. This is probably the trickiest point, and might be argued to rather be in present tense, though I personally don't think so.
• "notable discrepancies, which we discuss in more detail below": Here you are describing what you have written in the present article, that is, part of your own writing process. This should be in present tense.

Discussion Section of My Own Article

The respondents of our surveys and interviews gave us valuable responses that generally confirmed our hypotheses. We conclude from our analyses that the kind of people in our study generally act in the way that our hypotheses claim. However, the brain electrode readings give us a more nuanced understanding of our findings. They indicate that people act in that way only in certain circumstances. The appendix of this article provides more details on all this.

Here it gets quite tricky, with cases that might be argued either way. Comments:

• "respondents of our surveys and interviews gave us valuable responses": The respondents responded in the past.
• "generally confirmed our hypotheses": we conducted the tests of our hypotheses in the past. However, it could be argued to be "generally confirm our hypotheses", since the hypotheses remain confirmed eventoday and in the future by those historical tests.
• "We conclude from our analyses": Not only in the past, but now and in the future, each time we reassess our analyses, we continue to arrive at the same conclusions.
• "our hypotheses claim": Our hypotheses have not changed; they continue to make the same claims.
• "people in our study generally act in the way", "people act in that way": We extrapolate our findings not only to the people who responded in our study, but as a general finding concerning how that type of person continues to act.
• "the brain electrode readings give us a more nuanced understanding of our findings", "They indicate that": We are referring here not to the past fact of taking the readings, but to the ongoing fact of our interpretation of those readings.
• "The appendix of this article provides more details": This refers to a supplementary section of my own writing.

Appendix of My Own Article

In this appendix we provide more details about the analyses from the study. We conducted even fancier and more experimental analyses to better understand the results. Our supplementary analyses revealed some cases where the general trend did not apply. We explain our interpretation of these supplementary findings in the Discussion section of the article.

Comments:

• "In this appendix we provide more details": This is the writing process of the current section of the article.
• "We conducted even fancier and more experimental analyses", "Our supplementary analyses revealed some cases": These are procedures conducted in the past.
• "the general trend did not apply: This is a past finding from a past analyses. It might be argued to be an interpretation, in which case it should be in present tense.
• "We explain our interpretation of these supplementary findings in the Discussion section": This reference to the main body of the article should always be in present tense, since it is written in an appendix.