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I am writing a paper in the mathematics field, and I found out that very often (too often) I begin sentences and paragraphs with the word "first".

For example, "First, define P as the string..."

I wondered if there is any good alternative for this word, or maybe even a rephrasing for the sentence. I'd rather not use other words from this family as well. (Firstly, At first, etc.)

Thanks!

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    I would ask yourself a couple of questions: 1) Are you sure you do this too often? If each section only has one 'first' thing, your readers probably won't notice. 2) Do you need to replace it with an alternative word, or could you just leave it out? What about 'Let P be the string...'? – DM_with_secrets Apr 28 '20 at 11:10
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    Also, what field of mathematics? I think whether @Chronocidal's answer is appropriate for your situation or not depends quite heavily on that :) – DM_with_secrets Apr 28 '20 at 11:17
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    Theoretical computer science. I am using it every other paragraph. The idea of leaving the word out seems to work in many cases :-) – Michael Apr 28 '20 at 11:38
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On the one hand, this will depend on which usage of "first" you are employing. On the other hand, you have provided us with an example sentence.

Initially, you could say "to start with", or "to begin". Working from the assumption that you are listing steps in a process or algorithm, you can commence by deciding if it is even necessary to use full paragraphs:

1) Determine if bullet points or an enumerated list makes the point clearer

2) Consider the possibility of lines of pseudo-code or a flowchart

3) For each sub-task in isolation, GoTo 1

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  • In general this would be good advice for a process or algorithm, as you say, but given OP's context (a mathematics paper), I'm not sure whether it's quite appropriate. I guess it depends what sort of mathematics... – DM_with_secrets Apr 28 '20 at 11:16
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    @DM_with_secrets Agreed - in some fields, a "paper" is essentially a 1-line introduction, followed by 20 pages of formulae... – Chronocidal Apr 28 '20 at 11:23

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