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I have helped a scientific(math) author to find a reference and I have corrected several errors in his paper. Should he acknowledges me when he publishes his paper? Will that affect my academic career positively or negatively? And if he doesn't acknowledge me what can I do?

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    Under the circumstance that you described, I think the author should acknowledge you, but I also think you shouldn't care much whether he does or not. Acknowledgements are unlikely to help advance your career or status. – Andreas Blass May 1 '20 at 16:11
  • @Andreas Blass Thanks a lot for your reply! – E.s. May 1 '20 at 18:41
  • @Buffy Thank you for editing! – E.s. May 1 '20 at 18:42
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should he acknowledges me when he publish his paper?

Acknowledgments are discretionary, so they needn't acknowledge you.

Will that affect my academic career positively or negatively?

Any impact will likely be minimal.

And if he doesn't acknowledge me what can I do?

You needn't do anything.

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    @E.s. Helping-out might not be considered as contributing. – user2768 May 1 '20 at 11:49
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    If you corrected mistakes in his math you should be a coauthour. If you corrected writing you don't require any acknowledgement. You did a favor. – user120011 May 1 '20 at 12:54
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    @E.s. If you contributed intellectually by correcting the math in the paper in a way that is more than just typography you should be a coauthor. The other things you have described are favors. – user120011 May 1 '20 at 14:32
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    @CJR I'd say authorship goes beyond more than just typography. An intellectual contribution is certainly required, but not sufficient, for me. It's difficult to provide a general quantification though. – user2768 May 1 '20 at 16:21
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    The usual standard for co-authorship is to "intellectually contribute" to the material. That means being part of the hypothesis formulation, experimental evaluation, theoretical development, and/or statistical assessment. Finding a reference is not an "intellectual contribution". – Wolfgang Bangerth May 1 '20 at 16:55

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