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The quote in question comes from the Introduction, page 12, to this book:

In our quest for comprehensiveness, we have chosen to present all the basic elements of cryptography needed to understand the complexities of Monero, and their mathematical antecedents. In Chapter 2 we develop essential aspects of elliptic curve cryptography.

I have found that develop can mean to discover, find out; to uncover. Is it the intended meaning? If so are there any other resources that would corroborate such meaning of develop? I cannot help thinking about rewriting this sentence with another word, such as cover or discover, like so:

In our quest for comprehensiveness, we have chosen to present all the basic elements of cryptography needed to understand the complexities of Monero, and their mathematical antecedents. In Chapter 2 we cover essential aspects of elliptic curve cryptography.

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    Whether you like it or not, this terminology is common in mathematical exposition.
    – GEdgar
    Sep 27, 2021 at 12:01

2 Answers 2

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One common enough use of this verb in scientific literature is the following, where mostly "explanation" is concerned, the addition of ideas is not a constructive addition but an addition of known facts that haven't yet been mentioned.

(OALD) idea/story/musical theme ​[transitive] develop something to add further explanation or details to an idea, story or musical theme
SYNONYM elaborate
♦ She develops the theme more fully in her later books.
♦ The piano then takes up the melody and develops it.
♦ He began to develop these ideas in a series of paintings.

In your sentence this is not exactly the meaning that is intended; it is not either the following, plain meaning.

(OALD) ​ [intransitive, transitive] to gradually grow or become bigger, more advanced, stronger, etc.; to make something do this

The exact meaning is not found in this dictionary, but it appears in the SOED (Shorter Oxford English Dictionary)

(SOED) develop 2 Uncover, reveal (something immaterial or (obsolete) material); make known, bring to light; discover; detect, find out. Now US. [since] mid 18th century

Since this book seems to be issued from American authors, the "Now US" label, which means "only used in the US nowadays", makes it the most likely meaning (essentially, "reveal", "make known", "bring to light").

This is a definition very similar to the one found in the Merriam Webster dictionary, which is an American dictionary, but that you do not find either in OALD, Collins, or lexico which are British dictionaries.

a: to set forth or make clear by degrees or in detail : EXPOUND develop a thesis

This is so a fortiori because "aspect" in the case of a scientific phenomenon is not an appearance that could be more or less changeable but a fixed feature that one is not likely to change unless the theory is reckoned with as lacking in some respect.

It is true that the connotations of the plain meaning are not so pleasant but it is also true that the shift from this plain meaning to the relevant one is an accomplished thing. If one finds those connotations too spurious one can use the prepositional verb "to cover", or the more literary and imaged "discover".

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  • Methinks the intended meaning of develop in the original quotation is not develop something to add further explanation or details to an idea, story or musical theme. The meaning that you cited from SOAD, Uncover, reveal [...], seems to be the one used in the original quotation. One might find this meaning in wiktionary as well: To discover, find out; to uncover. This meaning is described there as now rare. This rarity along with the lack of exposure on my part well explains my discomfort.
    – John Smith
    Sep 27, 2021 at 18:39
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    @JerzyBrzóska Well, yes, lack of familiarity, but all the same, a need to change to "cover" because "develop" would not be exact… It seems to me that this blunt rejection is due to an initial (erroneous) acknowledgement that the idea in "develop" is that of making the aspect more extensive; isn't it so?
    – LPH
    Sep 27, 2021 at 18:55
  • It is so, that initial acknowledgement was erroneous.
    – John Smith
    Sep 27, 2021 at 19:02
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Have a look at this definition:

4a: to cause to evolve or unfold gradually : to lead or conduct (something) through a succession of states or changes each of which is preparatory for the next

/developed his argument

From here

Unlike cover, which is straight forward and just means include, talk about, develop carries the idea of gradually building up from the fundamentals and taking the reader through the process of discovering or working it out.

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  • I do agree with this definition, yet methinks discover or uncover would fit better. My intuition tells me this, the same way seems to would read more natural in my comment than methinks, although the latter in not necessarily incorrect.
    – John Smith
    Sep 27, 2021 at 9:23
  • Perhaps, @JerzyBrzóska, your discomfort is rooted in a questionable assumption that things to be known are eternal realities independent of their knowers.
    – Brian Donovan
    Sep 27, 2021 at 12:12
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    @BrianDonovan That is not the point; the discomfort is rooted in the connotations carried by the factual meaning, which implies an evolution. As the word is used in the sentence no matter of any evolution of what is being treated is considered, as it is more or less an eternal reality, but instead evolution is embodied in the process of unfolding to the reader the hows and whys of this reality. I tend to believe that it is the impossible or uneasy dissociation from this first (connoted) evolution that is the cause of his/her disturbing impression.
    – LPH
    Sep 27, 2021 at 16:17
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    One way to look at it is that the text book is leading you through a didactic process to communicate existing knowledge. It is not uncovering or discovering new facts: it is an educational program in which knowledge and skills are developed in the reader. Another way to look at it is that textbooks use their own terminology which is often slightly strange and students just have to accept it.
    – Stuart F
    Sep 27, 2021 at 16:34
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    @Jerzy Brzóska while methinks is definitely more bookish, I wouldn't say it's unnatural at all in your sentence and it did not jump out at me at all when I read it before you pointed it out. I think it's just a question of exposure to that usage, if you're unfamiliar with it, it will seem strange until you've seen it enough or used it yourself. Using developed in this sense is definitely well-established in literature though.
    – Curiosity
    Sep 27, 2021 at 17:42

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