Which tense to use in an academic paper when referring to past research?

I am writing a paper in mathematics.

Stone theorems have a long history. B [B78] proved the stone theorem for the B model. C and D [CD14] not only prove a stone theorem for the cake process in random environment, but also have a nice overview of existing results.

(here B, C and D are some names, and 'stone theorem' and 'the cake process' also represent something else, but it is not important for the structure)

Question: is it ok to use a past tense in the first sentence which refers to 1978, but use a present tense in the second sentence which describes something that happened relatively recently, in 2014?

Answer

It's perfectly fine to use the present tense for all research, even going back to ancient times; see here for another question about this.

However, there is a way that you can usefully shift tense in a literature review in a scientific paper. You can use the present tense for recent research that is still a topic of current conversation—especially if your paper extends or contradicts that research. The cut-off point for "recent"—that is, the present—is "present conversation". The present perfect is a convenient way to suggest that the matter is still "open" and that your paper is going to make a contribution to it.

For example, if your paper proves a new stone theorem for the cake process, you could choose the tenses in your literature review like this:

Stone theorems have a long history. As long ago as 1978, B [B1978] proved the stone theorem for the B model. More recently, C and D [CD2014] have proved a stone theorem for the cake process in a random environment. They also provide a nice overview of existing results. In the present paper, we prove that stones in non-random cakes are indigestible.

The past tense suggests that B1978 is mostly of historical interest, a settled matter, now forgotten, or extremely well-known. It's done. Switching to the various forms of the present tense suggests that the research in those tenses is more directly relevant to the "present" paper—that is, yours.

This trick will probably have no effect on non-native speakers, who are usually oblivious to the difference between the simple past and the present perfect. And most native speakers do not consciously understand how they exploit these differences in tenses. But it's a very common technique at the beginning of a presentation to establish the scope of what is to follow. It sets the reader's expectations, even though most readers (and authors) aren't aware of it. You can see "establishing tense" used a lot at the beginning of newspaper stories, where an opening statement in the present perfect tense often indicates the range of time that the story will cover ("Election costs have risen 300% since 2000"), while an opening statement in the simple past tense often suggests a very short time-frame ("Stocks rose 2.1% on light trading [implicitly today].").