“Something suffices the condition that” vs. “it suffices that something”

Question

In a book I am reading there is a sentence:

Our initial version of Cauchy's theorem begins with the observation that it suffices that f(z) [a function] have a primitive in a region Ω

In this sentence, I think the author wants to say

f(z) suffices the condition that it have a primitive in the region Ω

but I don't understand why the author writes

it suffices that f(z) have a primitive in a region Ω

Answer 1

No, you cannot say that “it suffices the condition”. That is not English.

The author is saying that “it is enough that f(z) have a primitive in a region Ω” for such and such a thing to be satisfied or hold true or apply. Something like that.

Note that we have moved into the hypothetical havens of that rarefied domain known as the subjunctive: “if suffices that the function have a primitive”. Only the very most careful of speakers (or writers) speak that way any more. But in this domain, it remains commonplace and indeed even expected. It is how things are done there.

That’s because mathematicians are even more precise than lawyers. These use language extremely — even exceedingly — carefully. When I was doing corpus studies of modern uses of the English subjunctive, mathematics treatises were the richest gold mine to be found for such rarities as these.

Mathematicians are exquisitely formal people, you know, when it comes to language use. It comes from having to formally define things as they artfully create their mathematics. This author wrote exactly what he meant to write. You must come to understand what it means, not try to rewrite it; otherwise you risk destroying what he has so carefully crafted.

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tl;dr: Suffice it to say, suffice is not transitive.

Answer 2

I think you are confusing the words suffice and satisfy. Suffice is an intransitive verb meaning to be enough, so

it suffices that f(z) have a primitive in a region Ω

means that

it is enough that f(z) have a primitive in a region Ω

Satisfy in the mathematical context means to fulfill. You can say

f(z) satisfies the condition that it have a primitive in the region Ω

Final example to make the difference clear:

it suffices that f(z) satisfy the condition of having a primitive in a region Ω