Suppose one wants to use a theorem that was published quite a long time ago (+80 years) in a paper that is using a terminology and notations that are very much out-dated (making the paper very hard to read). Is it okay if we want to reformulate the result as well as the proof in an article using a more modern language (of course giving credit to the original paper)?


Or, on the other hand, is it something one shouldn't put in a research paper, since it's not a new result ? What is the general policy for this kind of things ? 



Reproving a known theorem in an article
I don't think academic math comes up with general policies for things like this. The dreaded "common sense" should be applied. How well known is the old result, for example? Some things are very old but everyone knows them. 


Or..to give an extreme example: Suppose your result was little more than a corollary of an old obscure result. Writing up the old result in new language and then tacking your result on the end wouldn't look too good... So in such a case I would not include the proof of the old result and just accept that I had a very short paper.


The other extreme is that the old obscure result is fairly short and not too hard anyway, in which case people would believe you/be able to read the old paper if they really had to... so again I would not include the proof of the old result.


If you judge to be somewhere in between: that the old result is very relevant and is hard or subtle in some way but that doesn't overshadow your own work, then people will probably just be pleased to see a nice account of it.


