PI coauthorship on previous papers I independently wrote a number of math articles, and published some of them in refereed journals. I wrote the draft of the thesis, and contacted a Prof., and started a PhD program under his supervision. After being accepted, the supervisor


Asked me to change all notations and terminology. I hesitate, because I used the terminology in use in the domain, I kept at minimum new terms, and I already used these terms in the published papers.
Asked me to make him coauthor of some of the papers I haven't yet published, and which I wrote previously, without any suggestion or discussion with him. He motivated his request by saying that my articles need to be polished (ie terminology changed with an invented one), and that even when they will be ready, nobody will accept them with my name only (although I already published some articles as single author).


He is very assertive with these requests, and I feel like he is putting pressure on me. Normally, I would like to have him as coauthor, and maybe it will be good for my career. But I am affraid that he will make my results unrecognizable, and incompatible with the other papers in domain, including my owns. And, frankly, his only contribution is that he suggested to change the terminology.

What should I do?
We cannot tell you what the best decision is, but I get the feeling from your post that you already have some course of action in mind: politely decline, with your arguments, and if he insists too much, find another advisor. I would agree with that being the best solution for you, but only assuming that your assessment of the situation is correct.

Don't take it badly, but I have seen it happen before. An established researcher gives advice to a newcomer (or more junior researcher), who disagrees and concludes that such bad advice can only be motivated by self interest. That sure is one possible explanation, but another might be that the advice is (partly or fully) correct, but the student doesn't recognize it (yet). Take a second look at his advice... There can be good reasons to suggest nonstandard notation: trying to make the paper more appealing to the community of another field, by using their notations. Or making the case that existing notation doesn't properly cover the cases considered. Or maybe what you consider standard notation actually isn't, and you are currently using a notation used by a prolific research group (bias in your reading list).

I am not saying that it is your case. I'm only saying that you should seriously consider it before taking any action.