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This is a simple historical question about the origins of the English phrase 'natural numbers', and ancestor phrases in other languages containing words similar to 'natural'. My curiosity just stems from the obviously profound quality of both the underlying concept and the use of the word 'natural' to describe it. The issue of including zero is immaterial to my concern.

At the page below it gives an entry from Chuquet (1484) as the earliest instance but looking at the list of early references there it gives the impression that the word 'natural' for these numbers was in common currency around that time.

https://jeff560.tripod.com/n.html

I wonder if the Latin root 'natur-' was used for these numbers in Roman times, and whether the similar Greek phrase 'physical numbers' was ever used? In any case, can it be attributed to a single individual or did it appear to evolve naturally (sorry for the pun)?

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    $\begingroup$ It is not a phrase. $\endgroup$
    – markvs
    Commented Dec 25, 2020 at 4:21
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    $\begingroup$ @dodd Why do you deny that 'natural number' is a phrase? $\endgroup$
    – bof
    Commented Dec 25, 2020 at 5:34
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    $\begingroup$ I think this question is more appropriately asked at History of Science and Mathematics. $\endgroup$
    – JRN
    Commented Dec 25, 2020 at 5:42
  • $\begingroup$ A phrase normally is a part of a sentence, It is not always true, of course, Many people would view "Sh*t!" as a phrase. But according to Wikipedia, phrase is usually required to include all the dependents of the units that it contains. Some expressions that may be called phrases in everyday language are not phrases in the technical sense. For example, in the sentence I can't put up with Alex, the words put up with may be referred to in common language as a phrase but they do not form a complete phrase, since they do not include Alex, which is the complement of the preposition with. $\endgroup$
    – markvs
    Commented Dec 25, 2020 at 6:19
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    $\begingroup$ @dodd The online OED's definitions of 'phrase' include 2a. "A small group or collocation of words expressing a single notion" and 2c. "Grammar. A small, unified group of words (in a sentence) that does not include both a subject and a predicate or finite verb; (more recently also) a single word having an equivalent syntactic function; (gen.) any syntactic unit larger than a word and smaller than a clause." $\endgroup$
    – bof
    Commented Dec 25, 2020 at 11:47

1 Answer 1

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In the Oxford English Dictionary says [compare French nombre naturel (1675)].
The oldest example in English it has is from 1763. W. Emerson, Method of Increments, page 113:

To find the product of all natural numbers from 1 to 100.

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  • $\begingroup$ It does not answer the question. Must be before 1484. $\endgroup$
    – markvs
    Commented Dec 25, 2020 at 13:46
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    $\begingroup$ @dodd ... The question is about "the English phrase" as well as about ancestor phrases in other languages. That 1484 is the French phrase "progression naturelle". My answer is about the English phrase "natural number". $\endgroup$
    – Gerald Edgar
    Commented Dec 25, 2020 at 15:32
  • $\begingroup$ this 1763 quote, as well as a whole list of other quotes going back to 1484 is actually in the web page cited by the OP, I presume the OP is looking for earlier sources that are not listed there.... $\endgroup$
    – Carlo Beenakker
    Commented Dec 25, 2020 at 19:30
  • $\begingroup$ Euclid (the mathematician, not the city) used the term in his book. Being a Greek, he wrote φυσικός αριθμός. $\endgroup$
    – markvs
    Commented Dec 25, 2020 at 23:31
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    $\begingroup$ @dodd ... Euclid has no mention of the phrase "natural number". The OP is not about the concept, it is about the words. By the way, why are you commenting my answer, and not the original question? $\endgroup$
    – Gerald Edgar
    Commented Jan 3, 2021 at 19:17

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