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?