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In (pure?) mathematics, the order of the authors for a given paper is almost exclusively always alphabetical. This leads me to believe that there may be a similar convention when writing acknowledgements.

In what order should acknowledgments be written in a math paper? By order of importance (increasing or decreasing), by alphabetical order, or something else? Does it not matter?

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It generally doesn't matter much (though I wouldn't suggest using in increasing order of helpfulness), but if some people deserve special thanks they should be singled out. I'll often write acknowledgements in this sort of format:

  1. I thank Prof A for encouraging me to think about this problem and Prof B for the realization that it could be approached by X ("chronological order").
  2. I also thank C, D and E (alphabetical order) for useful discussions and feedback.
  3. This work was partially supported by Grant 12345.

If it's a co-authored paper you can separate sentences/phrases for specific thanks from each author.

Generally my advice on questions like this is just to look at a bunch of other papers, see what they do, and learn from that.

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