# Best way to write an equation while explaining something in a paper

I have found it difficult sometimes to write properly an equation in the middle of some explanations on a research paper, for example:

This can be rewritten by a change in parametrization a = m as,
E = ac²
which, then simplifies to,
E = a c × c.

I have seen people writing it in different styles. In this one, I assume that the equations break the flow of the sentence. So, I usually put a full stop after explaining the entire sentence. So, the w in which in my example in lower case.

Is there a conventional way to write things like this that is considered more scientific?

• This does not answer your question about the formatting, but your commas are misplaced. The correct placement is: ... $a = m$ as $$E = ac^2,$$ which then simplifies to $$E = a c \times c.$$ (Also note that you should not really use $$to display math in Latex. But maybe you are only doing this for the sake of simplicity here.) May 12, 2023 at 18:05 • Is there supposed to be a "where" somewhere in your example? Regardless, to quote David Mermin in What's wrong with these equations?, Physics Today 42 (10), 9–11 (1989);, "Math Is Prose" so equations really shouldn't break the flow of sentences. May 12, 2023 at 20:44 • @AdamPřenosil yes, i use$$ only here because of the stack exchange environment. Surprisingly, it doesn't work on this particular forum. Thanks for the suggestion anyway. May 12, 2023 at 20:57
• @Anyon Thanks for the nice suggestion and reference. I will look into this. :) May 12, 2023 at 20:58
• @Chris_abc Yes, certainly you don't want to start the line after the displayed equation with a comma. May 13, 2023 at 18:07

You treat mathematical equations like regular parts of prose. As a rule of thumb, your surrounding prose and formatting should be just as it would be if you replace all your equations with [thing]. If we do this we will see that your commas are all over the place and make for an awkward pacing of your sentence:

This can be rewritten by a change in parametrization [thing] as, [thing] which, then simplifies to, [thing].

A much better form would be:

This can be rewritten by a change in parametrization [thing] as [thing], which then simplifies to [thing].

Another thing to bear in mind is that modern mathematics can lean heavily on the benefits of standard mathematical notation making use of the transitivity of equivalence relations to give clear sequences of steps in a succinct notational form. While ancient mathematicians tended to present mathematical steps and implications using more prose, we can write them in a very succinct way like this:

Taking [thing] gives [thing].

For your particular case, you could write:

Taking $a=m$ gives $$E = mc^2 = ac^2 = ac \times c.$$