Dear Folks,

I have exchanged a few comments with user T. [whom I don't know, although I certainly believe is a research mathematician] and BCnrd [whom I certainly do know, as does most everyone here, I guess] in the following thread:

http://mathoverflow.net/questions/38190/values-of-zeta-at-odd-positive-integers-and-borels-computations

Essentially, a question made reference to a 2010 paper in a rather obscure journal which claimed to prove a certain result about zeta values. Somewhat ironically, the actual question was whether this result was known before. (I am not a true expert here, but as I expressed, I think it wasn't, and that such a result would be a big breakthrough.)

In one of the comments, T. explained mentioned some "indicators" that the paper in question was not correct: the author is not a professional mathematician and has few, if any, prior publications in math; rather his publications are in fringy topics; and he is 60 years of age.

I objected that saying such things was against the spirit of the site -- none of these things have anything to do with the paper itself. It's not that I disagree factually with any of the indicators T. gave (as I mentioned in a later comment, I myself did a google search and uncovered all of this information) nor am I urging anyone to draw a different conclusion from these indicators. I just think that it's not helpful to say "Based on circumstantial evidence, I think this guy's a crank." Referring to his age made me uncomfortable: maybe I'm too PC, but that struck me as being overtly discriminatory.

There hasn't been any support for what I said. What do other people think? Am I being too careful here?

I think negative comments about a person's age are indeed discriminatory and should not be intentionally propagated, especially if they insinuate that the person is a crank, and it is appropriate for you to object to such comments. There are more authentic ways to doubt any doubtful result.

@Pete: I agree with your stance. I think "It has been discussed on this site before that we are generally not interested in non-expert opinions on whether a paper is correct" might have come off a little harsher than you intended it.

@Andy, Cam, Dan: thanks for your support.

@Cam: I agree, the remark you quoted was terse and open to overly harsh interpretations. What I was getting at is that an "expert opinion" is not just an opinion by someone who happens to be an expert. Rather it is an opinion that makes use of that person's expertise. Maybe "professional opinion" would be a better way to put it.

@dan : I think that the sample size of people who write their first paper at 60 is too small to draw any conclusions (and I certainly can think of people who have done groundbreaking work but only got started in their mid 40's, for instance).

Come to think of it, the chance that a 22 year old makes a major mathematical breakthrough is pretty small too.

As a tangential point, I've personally met more than a few solid mathematicians involved in crypto and that sort of thing that don't exactly publish much or have an academic affiliation. If they pursue research that can be made available to the public later in or after the end of their careers their pubs would raise a lot of these sorts of red flags. OTOH, I can personally think of (and most of you can surely imagine) scenarios where it would make rather a lot of sense to perfunctorily disseminate (or if sufficiently easy, even formally publish in a decent journal) work that is clearly marginal or poorly written (though this is less true in math than other disciplines).

The work is the thing to evaluate. If a result is potentially important to you, you should be able--and willing--to understand if it is correct or at least plausible and say why or why not.

Euler's Elements of Algebra was first published in 1770 when Euler was older than 60. This is a textbook, not a piece of wholly original research, but as such it is undoubtedly one of Euler's more influential works. http://web.mat.bham.ac.uk/C.J.Sangwin/euler/ElementsAlgebra.html This is to be expected given Euler's great reputation during his own lifetime, including when he was young, but that does nothing to enhance the quality of the work itself, whether centuries ago or now.

@Dan : I'm not worried about legal issues. I just think that calling someone a crank on MO is a serious accusation, and if you're willing to do so, then you should be willing to associate that opinion with your professional reputation.

This isn't like the rest of the internet. I'm basically at the beginning of my career. and I've still met or exchanged emails with a substantial number of people who are active on MO. People who have been around longer know even more people. It would be pretty hard to impersonate someone here.

Of course, there are people who are active here who are not really part of the academic research community (eg undergraduates and amateurs), but I think that in most cases it would be inappropriate for them to accuse someone of being a crank.

As a side note, I think such accusations should be extremely rare. They are really only appropriate in situations like the one here in which a good-faith question was asked about cranky-sounding work.

@Dan : Being accused of being a crank on a prominent professional website like this could have a serious impact on someone's career. Because of this, I think that the utmost care must be exercised in doing so. An amateur does not have any "skin in the game", so to speak -- they would not suffer professional consequences if they accused someone unfairly of being a crank. Being downvoted on MO is not nearly enough of a potential consequence.

Let me put it another way. In the rare situation in which something needs to be described as cranky (rather than merely being downvoted/closed), it should be clear enough that a professional is willing to stick their neck out. If none are willing to do so, then maybe it shouldn't be done.

I don't think you should view this as a negative judgement about you. Having to police things is a burden, not an honor! This is the same reason that many people (eg me) are unwilling to serve as moderators. Personally, I'd rather just stick to math!