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I must say that I am shocked at the number of questions on this site that reads like the following,

"my advisor has stopped funding me"

"my advisor has been completely ignoring my emails"

"my advisor is stealing my ideas!"

"my advisor wants to be 1st author, when I did the majority of the work!"

"my advisor wants to add another student to the paper and this is unfair!"

I was wondering whether these pervasive problems go away, when one is doing mathematics research? I imagine that in math research, one has more control / ownership of their work, there's no lab to be a part of and contribute to, one's funding is typically in the form of teaching stipends, and the meetings are typically one-on-one, with no group meetings to attend.

Is a math PhD a better experience than a science PhD, in the sense that there is significantly less risk of working for a problematic, unethical, malicious scientist / professor who only cares about himself / herself?

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    Beware of two things: first, this site collects questions about pathological cases and not questions from all labs where everything works ok and the advisors do answer the questions of their students and behave ethically; second, the word lab is here used not only denote a science lab with different pieces of equipment, but also a computer lab, where you have only computers, that is, a situation that can be close to that of a math researcher. – Massimo Ortolano Aug 26 '18 at 15:16
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    This probably also varies by country. That said, my experience in math programs in the U.S. is nothing at all like this (4 different graduate programs throughout the 1980s and early 1990s, and yes I realize this many is unusual). For one thing, virtually no one was involved with publishable research except maybe near the end, and generally people bent over backwards in trying to be fair, at least this was my impression. Probably the most noticeable behavior remotely like this is the sometimes hypermasculine competitiveness common in math. – Dave L Renfro Aug 26 '18 at 15:23
  • Maybe I should ask a question "I like my supervisor and I'm getting a lot of good publications out. is this normal?" – Azor Ahai Aug 27 '18 at 23:06
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Keep in mind that the number of questions on this site doesn't give any indication of how common such issues are, since people usually only post when something is wrong. We don't hear about all the cases where everything is fine.

I don't know any reason why math advisors should inherently be better people than in any other field, and I don't know of any empirical data that attempts to measure this. However, a few of the specific issues you mention are perhaps less likely to arise in mathematics, due to cultural and structural reasons.

"my advisor has stopped funding me"

In the US, at least, the main avenue of funding for math graduate students is through teaching assistantships, since math departments teach a large number of service courses. Faculty who have grants can sometimes offer their students a research assistantship instead, so that the student doesn't have to teach. But a student really isn't completely reliant on their advisor for funding. Moreover, there typically aren't major expenses for the research itself (no expensive equipment, etc), so as long as the student is getting paid, research can continue.

(This is not necessarily the case in other countries.)

"my advisor wants to be 1st author, when I did the majority of the work!"

The general practice in mathematics is that all authors are listed alphabetically, and the concept of "first authorship" does not exist. As such, people don't bother to keep track of who did the "majority" of the work. So this particular issue doesn't arise in mathematics.

"my advisor is stealing my ideas!"

While individual departments may vary, I think there's a general sense in mathematics that a joint paper "counts" about the same as a solo paper. As such, if a student has contributed to a project, the advisor has no particular incentive not to include them as an author on the paper.

"my advisor wants to add another student to the paper and this is unfair!"

As above, it isn't any particular disadvantage to a student if another student is added.

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    I agree with most of this, except that in mathematics I think a joint paper published by a student with their thesis advisor is usually worth distinctly less than a solo paper by the student -- within the standard culture of mathematics, the former indicates an unusual amount of help. In my experience, it is more common for this to be violated in favor of the student, so that e.g. certain solo papers arising from student theses were largely told to the student by their eminent advisor. Our community seems bad at recognizing that there are still victims here...just not the student. – Pete L. Clark Aug 26 '18 at 15:37
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    Let me also say that the message conveyed by a student publishing with their advisor is not very clear. Does it mean (i) they are weak, (ii) they were strong enough to truly collaborate with their advisor to arrive at a result better than what either could have done independently, or (iii) neither, but their advisor is more honest with regard to putting their name on the paper if they were crucially involved with the work than the not-so-honest "standard mathematical culture"? Speaking for myself, I have coauthored papers with students under both (ii) and (iii). – Pete L. Clark Aug 26 '18 at 19:12
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    @JeffE: Certainly. On the other hand, funding isn't tied to any particular advisor, which makes it somewhat more possible to switch to a new advisor if the relationship with the current one isn't good - without having to worry about whether the new advisor has funding available. There are still issues involved in doing this - potentially having to start over with a new project, time limits, willingness of new advisor to spend time working with you - but taking funding off the table at least removes one complicating factor. – Nate Eldredge Aug 26 '18 at 21:16
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    @JeffE: The funding model also means math mostly avoids the situation where external funding for a project dries up, and the advisor has to cut off a student despite being satisfied with their progress - or where an advisor has to choose which of several satisfactory students to support because there's no longer enough money for all of them. – Nate Eldredge Aug 26 '18 at 21:19
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    I'll point out that most of the comments above are about "pure mathematics". In applied mathematics, these days, solo papers are rare. Student papers are almost always with their advisers, and often other collaborators as well. – Wolfgang Bangerth Aug 26 '18 at 21:21

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