# Usage of "it is" in formal, mathematical language

I have come across a scientific paper written by non-native speakers where some mathematical formulas are introduced by "it is". For example:

Proof of Theorem X. Assume xyz. [Long mathematical argument.] Then, it is x>0. QED

Now, I don't think I've ever seen this usage of "it is" elsewhere. Personally, I'd write something like "Then, x>0 holds" or "We have/obtain x>0" or, even more simply, "Then, x>0".

So, I am wondering whether this is idiomatic.

• It doesn't make sense to me (native speaker with half a degree in maths) Commented Mar 6, 2019 at 10:12
• Are my reformulations correct? A similar example I found in the same paper is "By Theorem XYZ, it is a*b=c". I guess this doesn't make sense either. I would replace "it is" with "we have", but maybe the latter sounds informal. Commented Mar 6, 2019 at 10:17
• All your reformulations seem good to me; also "we find". Commented Mar 6, 2019 at 10:26
• @JasonBassford I acknowledge the usage of "it is" in your last sentence. I'm not totally sure/convinced it is of the same kind as in the "mathematical" example in the original post, though. The doubt remains, afaic. Commented Mar 7, 2019 at 8:45
• If this theorem started with the premise that x, y, and z were mutually exclusively greater than 0, and was showing that it was x that was greater than zero, then "Then, it is x>0" being read aloud as "Then, it is x (that is) greater than 0" comes fairly naturally. On Maiaux's last point, though, this doesn't appear to be the usage here. Commented Dec 8, 2021 at 4:57

Quite late to the party, but submitting (an) answer in case it's helpful. I'm speaking as someone who's a native English speaker, has finished a BS in mathematics, and is doing research in CS.

"Then, it is x>0" is, at best, pretty off-putting.

In my experience, the grammar involved with mixing mathematical symbols with English sentences is in decent part determined by three things:

1. Utility in conveying meaning
2. Convention
3. Whether the word-substituted outcome is appropriate and grammatical

These factors play off of each other pretty heavily– for #3, for instance, the set of appropriate readings is very much a consequence of the first two points. In this case, the two typical readings of x>0 are:

• "x greater than 0"
• "x is greater than 0"

Neither of these readings works particularly well in "it is x>0", failing #3 (for one thing, my first thought when hearing this is "as opposed to what?"). However, there are situations where utility and convention win out- we've established it's not conventional, though, and from a utility perspective, there are numerous no-greater-effort replacements that are more common, including:

• Then, x>0
• Then, we have (that) x>0
• Then, x>0 follows/holds (although I might instead say "Then, it follows/holds that x>0")
• Then, x>0 is true/is the case (although I might instead say "Then, it is true/is the case that x>0")

Of course, it's true that, at the end of the day, the important part of a proof is that your reader understands it and there are no gaps in logic. Nevertheless, I would do a double-take on reading the end of that proof.