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How does the process of collaboration in math work ? Do mathematicians like to share their problems ? Can I do this by e-mail ? How to ask mathematicians if they want to collaborate in a math project ? I'm still learning more advanced math but these are questions I had in mind and didn't know where to ask.

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Do mathematicians like to share their problems ?

Usually yes. Published papers will often have open questions or conjectures to which authors worked on / or think worthwhile but does not have a solution. These conjectures sometimes even have corollaries provided by the authors.

Mathematicians also sometimes just "hand out" open problems that arise in their research, write them on their webpage or public chat rooms.

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Comments

It is still true that a majority of mathematics papers have only one author.

It could be that your first chance to collaborate in mathematics will be the collaboration between you and your Ph.D. advisor.

After others get to know your publications, they may be willing to collaborate with you.

Two (or more) mathematics students at the same university, who see each other frequently, will likely talk about mathematics; that may occasionally develop into a result worthy of publication.


addition on : "a majority of mathematics papers have only one author."
user3482749 doubts it. I still think it is true.

Searching for evidence. MathSciNet has 57,667 journal papers for the year 2000. There is a "Sort by number of authors", but I did not get it to show me beyond the first 2,000 ... that was still in the one-author portion of the list.

Trying a smaller sample.
I arbitrarily choose MSC classification 20, journal papers published in year 2000.
Total number: 1307.
Number with zero authors: 2. {one erratum, one corrigenda}
Number with one author: 783. About 60 percent.

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    Your first line seemed unlikely to me, so I checked, and it is in fact false. At the time of writing, there are 559 papers on the ArXiV's "new" feed, of which 153 have exactly one author (including one with an appendix by a separate author). Commented Mar 9, 2021 at 19:21
  • Concerning the data in the edit - here are some data points for the year 2020 rather than 2000: (number of journal publications with <= 1 authors/total number of publications): MSC 20: 577/1629; MSC 35: 1485/6930; MSC 46: 403/1277; MSC 47: 527/2218. This data supports @user3482749's claim: it's probably save to say that, today, the majority of math papers have at least two authors. (Admittedly, the MathSciNet database might not be complete yet for the year 2000 - but I don't see any reason why the number of papers that are not in the database, yet, should depend on their number of authors.) Commented Mar 9, 2021 at 22:50

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