And it is important that this feeling is mutual, as if one of the collaborators neglects the other, the other will faced with the dilemma: “The person, whos opinion I respect thinks I’m not clever enough”. Whether the solution would be to resent the collaborator or to get unsure about her/himself, one will stop to share ideas and it destroys the purpose of collaboration.

]]>Thank you for sharing your experience. I am glad that you provided a counterexample to my conjecture – I was hoping that counterexamples exist.

Another thought. I wonder if the perception of contribution is related to gender.

]]>Author 1: We need to prove that the estimate on the function is continuous with respect to the parameters. As we know it is differentiable, one can replace the pointwise estimate by the estimate on the integral of the derivative which is usually easier. Unfortunately, I have no idea how to get continuity with respect to the parameters for the derivatives either… I can recursevly express derivative via the function, but then we are back to proving the continuity in the parameter for the function, and it just goes in circles :-(.

Author 2: Yes, it seems difficult. I don’t think I can help you – I haven’t dealt with differential equations for ages, if ever. May be we can ask somebody …

Author 1: My God, you are right! It IS a differental equation. Then the continuity with respect to the parameters follows from the most standart theorems – I have taught it in Calculus III just a year ago.

After looking it up in a text book the lemma is proved. Author 2 considers his contribution close to zero. Author 1 thinks that Author 2 provided the main idea of the proof (as the original problem comes from a field which is far from Differential Equations).

]]>I think the difference depends more from the person than from the curcumstances, and a good collaboration is like a good marriage – requires wisdom and appreciation from all the participants (I can observe, when I’ve learned them better, that with all the differences the only common feature of all my collaborators is that they are all lucky in their marriages).

And, finally, we almost never discuss the contribution. If the discussion arrises because sometimes one of us feel that own contribution was too little, the other is simply reminding that it is not our last article and revokes the fourth Hardy-Littlewood rule (see for example https://www.math.ufl.edu/misc/hlrules.html ).

]]>They had to decide how to divide royalties on each thing of value. They held a special sort of auction.

For Thing of Value 1 they each, all the pros and the two administrators, wrote on a piece of paper the percentage that each should receive. Some numbers were easy. If pro #3 had done no work on this Thing, all the papers correctly showed his share as 0. But there were, say, two pros, plus the two administrators. And on the 8 papers the numbers did not agree. They posted all of the proposed divisions on the board (without the names of the proposers) and studied them. No discussion. And then they filled in a second ballot. This time the numbers came closer. Again, posted, studied, but no discussion. They continued for several rounds, until the numbers were a perfect match. And then they moved to the Second Thing of Value.

And it worked. I am still amazed that their numbers converged, but they did.

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