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In an acknowledgments section to a mathematical paper, one conventionally says the paper has benefited from "helpful conversations" with so-and-so that clarified matters in some way, started one's wheels in motion toward an idea, and so on.

It happens fairly frequently, though, that I email or otherwise approach a colleague I suspect may have some insight, only to have an unhelpful conversation. By this I mean that although the exchange is well-informed and pleasant, through no fault of the other party I am unable to gain anything from it mathematically and it has no bearing on what I ultimately publish.

In these situations, my correspondents have made the generous donation of their time, so I feel they ought to be thanked, but on the other hand the paper has not actually benefited. How should I acknowledge their contribution?

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    I was tempted to include in my Ph.D. thesis a line of the form "I thank XXX for his helpful advice and encouragement, and YYY for his advice." Fortunately, my adviser prevented me from actually writing that. – Andreas Blass Jan 30 '17 at 16:27
  • @AndreasBlass: there's a more subtle "I thank XXX for his suggestions on A, and YYY for discussions on B" – smci Apr 27 '18 at 22:10
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I agree with Anonymous Mathematician: There are lots of non-obvious ways to contribute to a paper, and it never hurts to be generous. But if they really did not contribute to the paper, then there is nothing to acknowledge in the paper.

If you really feel you owe them thanks for something that isn't a contribution to the paper, just call and thank them.

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    Here's a logical reason why I support this answer: I doubt the people who were trying to help by talking with you were doing it in expectation of being mentioned in the acknowledgments. – aparente001 Jan 30 '17 at 4:54
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I'd recommend being generous in assessing what counts as a contribution to the paper. If a conversation genuinely wasn't substantive at all (for example, it consisted of nothing but pleasantries over tea), then of course it doesn't deserve thanks in the acknowledgments. However, there are lots of ways of being helpful that do not directly lead to any of the content of the paper. For example, someone may explain a theory you don't end up needing, or might help you explore what turns out to be a dead end. These are still helpful contributions, because they let you discard dead ends and focus on more productive directions. Even just learning that an expert in X can't easily solve this problem has some value, because it tells you that your main obstacle isn't developing expertise in X.

One way to draw the line is to ask whether the conversation was obviously useless at the time. If so, then there's no need to thank anyone. If it seemed plausibly useful to you while it was happening, then it's worth acknowledging. The tricky case is when you were always skeptical but the other person thought it was worth exploring. In that case, you might as well give them the benefit of the doubt and offer thanks.

The one thing you shouldn't do is thank some people for "discussions" and others for "helpful discussions". It's fine for some parts of the acknowledgments to be more effusive than others, but you should never write it in a way that seems to imply that some discussions were unhelpful.

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    Would it be ok to thank the helpful for "helpful discussions" and the unhelpful for e.g. "sharing their knowledge and time"? – walen Jan 30 '17 at 11:21
  • @walen When you do stuff like that (depending on how good you are at it), some people will notice and draw (negative) conclusions and some (probably most) won't. It's not a good idea when you actually have positive feelings towards all of them (even though you are calling some unhelpful). – Nobody Jan 30 '17 at 15:19
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    What you can do is thank some people for "discussions" and thank other people for specific contributions (i.e. "ideas that led to the proof of Lemma 3.6"). – Alexander Woo Jan 30 '17 at 16:13
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    @walen No. The points made in the last paragraph of the answer are equally valid even if you don't use the word "discussion" for the unhelpful ones. There's still a subject of "I thank X and Y for talking to me. X was helpful; Y wasn't." – David Richerby Jan 31 '17 at 14:11

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