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I am a new Phd graduate. During my Phd I mostly worked and found my research problems on my own. I managed to publish some papers with my supervisor, even though he didn'd help much. I think that is not so uncommon. Now, after graduating, I work at a university and do research again "on my own".

In my view it is alright to do reasearch independently. The feeling of making new progress and publishing a solo paper is of course great. However, everytime I put a new paper on Arxiv, I am always afraid of making a serious and stupid mistake. In the past I did encounter such an experience. Before submitting a paper to Arxiv, i didn't sleep at all. I read the paper many many times since I am scared of overlooking something. I am obsessed with it for several days even after submitting to Arxiv.

Q1. What is an usual and easy solution for this situation?

Is it common to send out my preprint to an expert (for whom I do not know before) to have a look before we publicly submit it to Arxiv?

AskMathQ NoStupid
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    This may be a better question at the Academia SE. It seems more targeted towards that general community than just math. Regarding your question, I don't have much useful experience considering I'm just a high school student, but I would think that sending the preprint to an expert is a good idea. I don't think there's anything you can lose by doing so, and you could definitely benefit from that. – Varun Vejalla Sep 22 '20 at 21:52
  • I understand that Academia is a more general host for my question. However, I know that there are many mathematicians like me who mostly work alone (or not able to find a collaborator). So it is still reasonable to put this question in the context of submiiting a mathematical research paper to Arxiv. – AskMathQ NoStupid Sep 22 '20 at 21:57
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    In my experience sending out a preprint to an expert doesn't happen that often, and I personally wouldn't encourage doing that without a really good reason - you are essentially asking an expert to use their time on your problem and not get anything for it, while you are possibly getting a single-authored publication out of it. You don't have to submit to arxiv, you can submit directly to a journal; the peer-review process is confidential, and if you get an OK from the reviewers with a recommendation to publish, post to arxiv. – Randy Marsh Sep 22 '20 at 22:11
  • @RandyMarsh Ha, that was the exact opposite of my advice! I'll definitely take note from someone with actual experience in submitting/publishing papers though. If I ever enter academia, I'll make sure to keep this in mind. Thanks for the advice! – Varun Vejalla Sep 22 '20 at 22:40
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    Also keep in mind that mistakes happen and are natural in the process of learning. World-renowned experts make mistakes as well, e.g. when Wiles announced the proof of FLT, the result was celebrated worldwide, but the proof actually turned out to be flawed and it took 2 years to repair it. – Randy Marsh Sep 22 '20 at 22:59
  • One simple solution is to post on Arxiv only after the manuscript has undergone the first round of reviews. That will add some confidence that the original version had no blatant errors, although there are no guarantees. Most journals allow posting preprints as long as they do not include final revisions. And generally, your experience is not unusual, serious research is a psychological roller coaster. Even aside from publication, you put time and effort into a line of thought and then discover something showing that trivializes the whole thing, or makes it unworkable. – Conifold Sep 22 '20 at 23:09
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    To clarify: are you asking for a method to avoid mistakes in a solo paper? Or a method to reduce anxiety about possible mistakes? – Julian Rosen Sep 23 '20 at 01:28
  • Thank Randy and Conifold. I think your suggestions are quite workable. Dear Julian, any comment on either direction is valuable to me. – AskMathQ NoStupid Sep 23 '20 at 02:40

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