How to acknowledge unhelpful conversations 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?
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.