I am a postdoc in math who defended his Ph.D. a year ago. I have 5 papers where three of them were written by me(only author). I have always made some (minor) problems that the most referees (except one referee who read my paper and asked me to revise it; the paper is submitted international Mathematics Research Notices) reject my paper at the first, which make me really sad, then I fix them and submit other journals. On the other hand, I have two papers with some great mathematicians that the referees wrote nice reports. I would appreciate it if one could give me some advice for the following questions:
1)When I wrote a paper, then I put it in arxiv, and then I submitted it to some journal. I was wondering that I don't put the paper in arxiv anymore and submit it first and then if it is accepted, then I put it in arxiv.
2) When I was noticed that I made a mistake in my paper (by some referee or colleagues), I felt so bad as my paper has been in arxiv for a while and some mathematicians read it and they found out that I made a mistake. I was thinking that affects my reputation, e.g., I have this thing in my mind that they don't count me anymore as a good mathematician and never read my future paper because they think this guy always makes mistakes. This thought is killing me, in particular, I think since I made some mistakes in my papers, no one will read my future papers. I read my papers several times and checked, but there are still some problems, even I decided to ask some good to read my paper and then I add their name, but they said no.
I have neither a mentor nor a supervisor to help me. I would be grateful if I could hear some advice for my career.