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Doing mathematics is itself not stressful for most mathematicians, I don't think. But your working environment (e.g., pressure on getting a grant, publish-or-perish culture, and review for tenure) can make it stressful in various ways. Sometimes, a referee's report can boil your blood, too. Your personality may also matter, e.g., pressure on proving big results. Math is fun. But living as a mathematician involves more than just math.
You can ask the same question for clothing styles. No big deal to you and many of us. But big deal to some. As for the students asking about styles, if you're inexperienced, it may not be too surprising if you get worried about really minor stuff simply because you don't know it doesn't matter to many.
In your example, I think what the author means is "the only techniques known to me are X and Y," not "the only techniques known to humankind are X and Y." I would expect a proof or citation if the author does mean the latter. I see many authors put a cliché like "as far as the author is aware" or simply add something like "it appears that" to avoid this, which sounds to me better than making too strong a claim if taken literally.
@JeffE To a mathematician, the probability being 0 doesn't mean it never occurs. It's just that it almost never happens. en.wikipedia.org/wiki/Almost_surely
Most likely not unless it's an unusual case or some of the journals you published in have a different policy than many others. In any case, as I said in the first comment, you should read the legal document you or your co-author(s) signed, and if you are still in doubt, you should ask the journal(s) directly. Some journals do allow you to post the published versions on your personal website, your institutions' server, etc. But I don't know a journal that is fine with uploading to a large network that systematically distributes papers for free.
It should all be written in the copyright transfer agreement you signed before publication. If some things are not clear, you can always ask the journal. If your question is a very general one asking about all papers out there posted by the authors themselves, it depends. For example, there are high-profile journals that are "hybrid" in that they are in general non-open-access (so their papers look like tightly copyrighted by the publishers) but do offer an open-access option for each individual paper if the authors so wish. If your filed is EE, many IEEE Transactions are like this.
