When working on a research project, one tries to spend their time answering questions that have not yet been answered. There enters the terminology of "known" versus "unknown" results, which we generally take to mean whether a problem has already been solved. On the other hand, we know that mathematics is always a work in progress, including instances of "known" facts that have turned out to be wrong.

The proofs of some results are quite esoteric, requiring extreme specialization in the topic to be able to understand. It is feasible that a paper might be peer reviewed, accepted by the community, and its theorems entered into mathematical canon, only for everyone capable of following the arguments to then pass away leaving no apt descendants to maintain the knowledge. My question is whether those results are still considered "known." The deeper question is about the value of finding new and more accessible proofs for such results, such that they may be more widely known in the literal sense.

To make the question less subjective, let's focus on the etiquette of using this terminology. For a mathematician to publicly proclaim that something is "known," does it require them to have read and understood the proof, to know of someone who has read and understood the proof, and if the latter, must that person be alive? On the other hand, does "known" merely mean that a proof has been published in a peer-reviewed journal at some time in history, no matter how long ago?

**Post-closing comment**

Just as food for thought, notice how closing this question as opinion based is to say that there is no precise universal definition for the term "known," or at least, that there are some ambiguities to it. I find this interesting.

the proof, and from my comment you can infer that in my opinion the answer is "no". Regarding whether anyone has to know about the result itself, then I would say yes, but this kind of follows trivially, because the person stating the result (and claiming it's known) knows the result. $\endgroup$14more comments