"Assume that A = B" subjunctive?

Over on Math.SE, a question exists regarding the usage of the word "that" in the following sentences:

1. Assume that A = B.
2. Assume A = B.

A well-known author suggests that users elect Option 1 in mathematical writing.

A discussion arose whether or not Option 1 is perfectly acceptable usage of the subjunctive, with a caveat: that the glyph "=" be read "equal" and not "equals."

The author of the book in question also further suggested that the word "that" be used only if it helps parse a sentence, "Assume that A is a group" vs. "Assume A is a group." This point was less contended, but in the subjunctive discussion, contrary concerns also arose whether the usage "Assume A be a group" is correct archaically, is correct presently, or has never been correct at all.

First question: given that "Assume..." is functionally equivalent to necessity in mathematical writing, is the sentence "Assume that A equal B" a proper use of the subjunctive?

Second question: Is, or has ever been, the usage "Assume that A be a group" been proper conjugation of "is" in a properly-used subjunctive?

Third question: Is there anything structurally unsavory about the use of the conjunction "that" in the form "Assume that A equals B" (note the s)?

Solution 1:

1. Patterning of the subjunctive is becoming very spotty in English, but is generally restricted to subordinate clauses licensed by verbs of compulsion or persuasion. e.g., The court orders/requests/requires/prays that Thomas present himself for sentencing... [pray used in its legal sense]. In modern American English (I don't know about older English) the preceding sentence doesn't work with psych verbs like hope/wish/pray [pray used in its common sense] or cognition verbs like think/assume/believe/suppose. Note also that the modal use of were (e.g., Assume that Thomas were guilty...) is usually called irrealis, not subjunctive.
2. That is correct, but only because let licenses a complement clause with its verb in the base form. It doesn't have to do with the subjunctive. (e.g., The judge let Thomas delay the hearing... is clearly not showing subjunctive mood)
3. Nothing structurally unsavory, and I agree that the best guideline on omitting or using that is to improve parseability.

Solution 2:

Your “well-known author” doesn’t seem to know English very well.

The verb assume always takes the indicative in contemporary English. The correct formulation is:

I assume that he is coming.

And therefore, of

Assume that A is equal to B.

or likewise

Assume that A equals B.

You can find people who might say

Suppose it were otherwise; what would you do?

Imagine that it were different; what would you do?

But there aren’t many of those.

As for your second question,

Let A be a group.

Is perfectly grammatical.

Finally, on your last question, there is nothing whatsoever wrong with having a that there, any more than there is anything wrong with not having it there.

Edit

I suppose it might be possible that your writer is using assume as a substitute for let, making it a sort of auxiliary. It would therefore take a bare infinitive under that reading.

However, the OED presents no documented evidence of that sort of thing. The only thing of apparent relevance which the OED gives is this:

10. trans. To take for granted as the basis of argument or action; to suppose: a. that a thing is, a thing to be.

• 1841 Myers Cath. Th. iii. §25. 91 — To assume that we have the most accurate possible translation.
• 1868 Peard Water-farm. x. 103 — The entire length of our farm is assumed to be about thirty-two miles.

There you have documentation that it takes both that and a simple indicative is form: one assumes that a thing is such and such.