How to find out who firstly introduced a mathematical concept?

Question

I am wondering if there is any way that one can find out the introducer of a given mathematical concept. For example, if I want to write that "Reduced free groups were firstly introduced in Habegger, Nathan, and Xiao-Song Lin. "The classification of links up to link-homotopy." Journal of the American Mathematical Society (1990): 389-419.", I can only be sure that it has been discussed in the paper but how can I make sure that there is no earlier reference on reduced free groups (Maybe the same name has been used for a different mathematical object, but I am talking about the one introduced in the sense as in Habegger and Lin's paper.)?

Answer 1

Normally the author of the earlier paper(s) should somehow make clear if they introduce a notion or rather continue an investigation giving a reference. So, check what is written in that paper. You can than continue with that older reference, if there is one, until the process stops.

This is however not at perfect method since it would not catch if latter it transpired that some authors thought in error that something is new but it was not.

Another method to complement the first one is to look at what other authors write in the same situation in which you are in. (Or, to ask an expert in the field.)

If in various sources nobody ever mentions anything else earlier, you can assume this is it. In any case you did your due dilligence. It is still possible that something was overlooked by everbody, and there are cases where things were overlooked for decades, but this is rare and there is no practical way in which you can exclude this happening to you.