A mathematician with a philosophical view of their subject will either be a realist or anti-realist (in ontology).

A realist might ask "Who discovered theorem X", while an anti-realist might ask "Who invented theorem X".

Q : If one wished to remain neutral philosophically, what verb would be an appropriate alternative?

(I thought identify would to the trick, but a friend of mine insists that identify strongly suggests discovery.)


Please note that I am asking about the general case here. I have given the statement of a theorem as a particular example of usage. I could equally have given the example of a mathematical definition, relation, "object", theory, etc..

  • My first instinct was "codify", but none of the definitions I've found seem appropriate. May 15, 2018 at 20:34
  • @KamilDrakari Thanks for your suggestion. I think "codify" strongly suggests "formalise" and formalism is philosophically "anti-realist".
    – epsilon
    May 15, 2018 at 20:40
  • 2
    You could say they "first articulated" theorem X.
    – user252684
    May 15, 2018 at 20:46
  • @PaulDirac Interestingly I have used "articulate" in this context, and it works well in the context of a theorem. However, it does not work in the general case. E.g., one would not say Hamilton articulated quaternions.
    – epsilon
    May 15, 2018 at 20:48
  • I would think that 'state' would be non-commital about whether something existed, or not, before it was stated.
    – Nigel J
    May 15, 2018 at 22:21

2 Answers 2


I don't think there is a completely general answer. As noted, "articulated" could work in some contexts. In other cases "described", "noted" or other similar terms might be more appropriate.


There seems to be a piece of this that's missing. Why would a realist use "discovered" while an anti-realist would use "invented?" To appreciate this, definitions of each word, and a synopsis of the philosophies, would need to be provided. Without understanding that, it's difficult to understand the distinction.

But from looking at the two words, and the "classification" of some suggested synonyms, it at least appears to me that realists concern themselves with with verbs divorced from intention. To "discover" something could also be to "stumble upon" something. Meanwhile, anti-realists concern themselves with verbs associated with intention. To "invent" implies deliberate effort.

Therefore, if I can use such expressions, realists are objectively passive, while anti-realists are subjectively active.

What you're looking for, then, is a verb that either combines both qualities or neither quality. But I'm not sure if that's possible. Especially if you want something that applies to all subjects. There may be no choice but to use a verb that comes down on one side or the other.

(I could propose any number of additional synonyms—identified, determined, expressed—but all of the things that make the other synonyms inappropriate would apply to these as well.)

My intuition tells me that, in order to use something that really distances itself from either perspective, a rephrasing may be necessary:

Who is considered to be the founder of X?
Who is the most famous for X?

Neither of these necessitates an explicit chain of events. While the meaning between the two differs, and neither means the same as "discover" or "invent," I don't think there can be something exactly the same as "discover" or "invent," that is completely neutral across all usage.

  • Thanks for your answer. You have made some interesting points, so +1 for that. Ultimately, I think you may be right to suggest that usage will be context specific.
    – epsilon
    May 16, 2018 at 16:48

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