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What is considered good style for writing small numbers as words or digits in mathematical texts?

I have three concrete examples, are there any differences between those?

  1. "M is a matroid of rank six" vs. "M is a matroid of rank 6"
  2. "There are six elements in the set" vs. "There are 6 elements in the set"
  3. "The numbers a and b differ by one" vs. "The numbers a and b differ by 1".

Are there any general rules?

Edit: Not to influence your answers, but I'm asking the question because a copy-editor of the London Math. Society changed all the above to use the digits while we had words in our manuscript. I'm not a native speaker, but I usually use words for small digits.

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In most cases, style guides favour words over numbers below a certain amount (that amount differing with the style guide, but commonly around a hundred) or precision (again, varying with the style guide, but one might have e.g. "a half" while also having e.g. "0.03").

With mathematical writing, and other technical and scientific contexts though:

  1. The number has a value to the understanding greater than in other writing.
  2. The cases where a style guide would favour digits are likely higher in the text as a whole, and using digits throughout will likely read more consistent.

With the last case in particular, even for non-technical cases, we would not mix highly, e.g.

They increased the amount from ten to a thousand and thirty-nine.

They increased the amount from 10 to 1,039.

?They increased the amount from ten to 1,039.

The third would likely not be favoured by many.

So, bearing these two points in mind, it makes good sense to strongly favour digits over words.

It is though, a matter of style rather than correctness, so a given style guide might insist otherwise, but do check if there are exceptions or allowances made by that style guide for technical matters.

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In each of the cases you cite, the use of words is better than the use of numbers. In general, style guides will recommend that you use numbers for "counting purposes" only when the written-out form uses more than one word (up to 20) or two words (up to 100).

However, if your number is some sort of measurement, such as "6.0 cm" or "6 cm," then you should not use words—the numbers indicate that it's a scientific measurement in a way that is not correctly captured with words.

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IMHO, if the numbers are part of the math, it should be always in digits. So I would put all these three cases in digits.

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    What does it mean to be "part of the math"? Why is "six elements in the set" part of the math?
    – Peter Shor
    Commented Jun 10, 2014 at 12:42
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    @PeterShor Here is I argue that "six elements" is part of the definition of the set. For a non-math example, "Let us pick up two elements from the set."
    – Ma Ming
    Commented Jun 10, 2014 at 14:15

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