# When writing in math, do you use a comma or colon preceding an equation?

This is a general question about mathematical writing especially for writing research papers and the like.

Question: Do you precede an equation with a comma or colon?

Example A:

1. The following equation is the Yosida-Hawking-Penrose-Dantzig function
2. The following equation is the Yosida-Hawking-Penrose-Dantzig function,
3. The following equation is the Yosida-Hawking-Penrose-Dantzig function:

Example B:

1. In fact, we can express the earlier function using a much simpler expression

where $\varphi(x,y)$ is the Demiane functional
2. In fact, we can express the earlier function using a much simpler expression,

where $\varphi(x,y)$ is the Demiane functional
3. In fact, we can express the earlier function using a much simpler expression:

where $\varphi(x,y)$ is the Demiane functional

Can anyone comment on which one is the best practice?

Generally, I would treat the equation as if it were any ordinary noun phrase, and use the usual rules for comma, colon, or no punctuation.

A colon is used if the equation is an elaboration, or an item. So, just as you might write

Lips are characterized by the following properties: fleshy, paired, red.

you would write

An ellipse is characterized by the following equation:

A comma precedes a non-restrictive clause (one that describes rather than identifies the noun phrase), so by analogy with

The line can be assigned to a simpler character, Polonius.

we might write

A line can be described with a simpler equation,

In comparison, with a restrictive clause, we use no comma, so just as we would write

From this, the oiler obtained the formula CH$_3$C$_6$H$_4$C$_2$H$_5$.

we would also write

From this, Euler obtained the formula

I suspect there aren’t any hard and fast rules for this, however. Whatever you choose to do, be consistent and reasonable.

ETA: You’ll notice that I have no periods at the ends of these equations. The papers I have generally (though not universally) observe this pattern. However, in other fields, equations may have ending punctuation depending on how they occur within a sentence. It may be useful for a writer to consult the publication’s style guide, if applicable, or at least examine previous articles within the same publication or outlet.