Contacting an eminent mathematician I have recently started a PhD. and am researching an area that two now eminent mathematicians devoted considerable time to in the 1980s. However, there appears to have been fairly moderate focus on this research area in the intervening years, and I have a question regarding one of the papers published by these authors nearly 25 years ago that nobody I have talked to has been able to answer. 
My question is, what is the etiquette regarding contacting the author of a journal article? Obviously one would only contact them regarding issues when all other channels had been exhausted, but in such circumstances or any other, is contact justified, or is it regarded by authors as a nuisance - as the question to them may well seem trivial in nature?
If anybody is able to shed any light into the issue of when they would feel comfortable (as a PhD. student) contacting an author, it would be very greatly appreciated.
 A: Let me separate your question into two parts, and note that some good advise is already given in the comments to your questions.  
First, you are concerned with the status issues and the age issues (student vs. professor, recent work vs. old classical papers, etc.)  I think math is pretty egalitarian, so the status issue should not be an obstacle.  The reality may be different, but often it's not an ethical issue - some senior faculty tend to be busier than grad students...   Similarly, to a lesser extent, math is timeless.  Unless the older work has been subsumed/trivialized by later far-reaching developments, I don't see this as an ethical obstacle either.  Of course, some people retire, leave the area or mathematics altogether, die, join NSA, or stop communicating with the outside world, but that's just life.  
Second, perhaps the more interesting part of your question is whether it is ethical to ask a clarification of some argument, complete proof of the lemma, etc.  While others might emphatically say "yes", I think this is less clear.  As with food or diet, I think this is good in moderation, but bad in large amounts, and the line is really easy to cross, and when that happens it's unpleasant for everyone involved.  
To make another imperfect analogy, let's compare math papers with children.  While the parents are of course completely responsible for their behavior when they are very young, as they move into adulthood this is less clear and eventually not true.  While the line in this case is hard to draw (it varies in different countries and cultures), when it comes to papers there is a clear line: the publication date.  In my opinion, while the paper is in the preprint form, the default position is that the author is responsible for all that's in the paper, as it undergoes public scrutiny. She/he really should answer and explain unclear/difficult points, unless there are compelling reasons not to do that (say, a followup paper with a better exposition).  But after the publication date, it seems the author may answer only if he/she wishes to, and the default position is that "somebody studied the paper and agreed with eveyrthing in it".  I know, life is more complicated, the authors and referees make mistakes, etc. but that's life again.  My point is that you should not get upset if the author refuses to comment on a published paper.  
A: While I was an undergraduate I once asked Gilles Pisier about an "obvious" proof in one of his articles (I plainly wrote: "Dr. Pisier, how did you get this?"), and he very kindly provided it. He even tried to answer me in Spanish!
A: The answers to this question are probably useful:
When and how is it appropriate for an undergraduate to email a professor out of the blue?
