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Corrected a small typo with possibly outsized impact
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Steven Stadnicki
Steven Stadnicki
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  1. It's the ethnicalethical thing to do.
  2. It's the polite thing to do, like sending a "thank you" note.
  3. Someone who helped you might expect it, and might feel snubbed if they see your paper without it. Relatedly, acknowledging someone's help might deepen your relationship with them, make them more likely to help you again, potentially lead to a collaboration someday, etc. Just like with "thank you" notes.
  4. A culture of acknowledgements helps make our field more cooperative and less competitive.
  1. It's the ethnical thing to do.
  2. It's the polite thing to do, like sending a "thank you" note.
  3. Someone who helped you might expect it, and might feel snubbed if they see your paper without it. Relatedly, acknowledging someone's help might deepen your relationship with them, make them more likely to help you again, potentially lead to a collaboration someday, etc. Just like with "thank you" notes.
  4. A culture of acknowledgements helps make our field more cooperative and less competitive.
  1. It's the ethical thing to do.
  2. It's the polite thing to do, like sending a "thank you" note.
  3. Someone who helped you might expect it, and might feel snubbed if they see your paper without it. Relatedly, acknowledging someone's help might deepen your relationship with them, make them more likely to help you again, potentially lead to a collaboration someday, etc. Just like with "thank you" notes.
  4. A culture of acknowledgements helps make our field more cooperative and less competitive.
Post Made Community Wiki by Todd Trimble
added 466 characters in body
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David White
David White
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In general, when faced with these kinds of questions, it's a good idea to ask your advisor and to check out what the norms are in the main papers you build on. In my experience, most single-author papers use "I" in the Acknowledgements, or sometimes "the author." Even with multi-author papers you sometimes see "The first author would like to acknowledge..." which makes sense because both of the authors are humans who have different people they want to thank.

In general, when faced with these kinds of questions, it's a good idea to ask your advisor and to check out what the norms are in the main papers you build on. In my experience, most single-author papers use "I" in the Acknowledgements, or sometimes "the author." Even with multi-author papers you sometimes see "The first author would like to acknowledge..." which makes sense because both of the authors are humans who have different people they want to thank.

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David White
David White
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This question was asked some time ago, but never received an answer. It has several highly upvoted comments, but there is also disagreement in the comments. I think the question is reasonable, given that writing Acknowledgements sections is part of the research process. This question probably could have been asked at academia.SE or MSE, but other fields do tend to use "we" a lot less than math.

First, there are zillions of writing guides online for math. Most agree that "we" is more common than "I" in the main body of your paper (see 1, 2, 3, 4). Reasons given include:

  1. History/culture in math
  2. The author is guiding the reader on a journey, like giving them a tour. The use of "we" brings the reader into the story and makes them an active participant. After all, the reader should be actively following along, checking that things make sense, etc.
  3. "We" is more humble than "I" - if an author says "I have now proven Theorem 2" it makes it look like the author did it all by him/herself, from the axioms. But remember that we all stand on the shoulders of giants. Using "we" emphasizes that math is a collective endeavor.
  4. Relatedly, using "we" emphasizes the results not the person who proved them. Again, that's relevant for readers in the distant future. The idea is that we're building up mathematics as a collective endeavor.

Note that this is not mandated. There are plenty of times when "I" (or another singular like "the author") is appropriate or even preferred. A great example is when you failed to do something, e.g., "The author believes it should be possible to drop the hypothesis that ... but has been unable to prove the result in this generality." This is related to point (3) above. With any writing, the golden rule is think about your reader and do what's best for the reader.

All that said, for Acknowledgements in a single-author paper, "I" is definitely the norm (see 1, 2, 3). The reasoning is that the Acknowledgements section of your paper is personal to you. It's not about the journey with the reader. The point of acknowledging the help you got is:

  1. It's the ethnical thing to do.
  2. It's the polite thing to do, like sending a "thank you" note.
  3. Someone who helped you might expect it, and might feel snubbed if they see your paper without it. Relatedly, acknowledging someone's help might deepen your relationship with them, make them more likely to help you again, potentially lead to a collaboration someday, etc. Just like with "thank you" notes.
  4. A culture of acknowledgements helps make our field more cooperative and less competitive.

Since the Acknowledgements section is the main section that's really personal to you, I think it's a great time to show the reader your humanity. Showing our humanity helps combat the idea that math can only be done by a few geniuses who are born with that innate ability. It's encouraging for young people to understand that everyone struggles, that it's normal to ask for help, etc. Acknowledging a helpful interaction with a junior mathematician can also be encouraging for them, make them feel like they are part of the math community, and help them get their name out there at the start of their career. Plus, it can deepen your relationship with that person as mentioned above.