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Or should one accept the stance that MO is not a place to multiplicate "nice" pieces of mathematics?
In my view, EMPHATICALLY yes. Write a blog post, and see what happens. This is not a group blog.
I don't think MO should be a pure "advertisement space". The reason why MO gets people reading its pages is because people are asking questions they really want to know the answer to. Dilute that and less people will bother with the forum.
If you have an actual question that you want to know the answer to, and you've done due diligence to ensure there isn't an easy answer available, by all means cook up a good question. Many of Joseph O'Rourke's questions strike me as being kind of like this -- he's interested in what people think about certain famiilies of ideas. He cooks up some juicy examples (usually with excellent graphics) to get people hooked on the problems as well.
<blockquote> But no other mathematical forum attracts so many visitors. </blockquote>
Not true at all, I'd guess. I bet more mathematicians glance at the Annals of Mathematics than at MathOverflow. Does it follow that your posting should be pulished in the Annals of Mathematics?
Not true at all, I'd guess. I bet more mathematicians glance at the Annals of Mathematics than at MathOverflow. Does it follow that your posting should be pulished in the Annals of Mathematics?
That would be something, l0l.
How about a pointer to an example in another SE forum "sharing knowledge"?
The stackexchange network explicitly allows asking and answering your own question to document an answer you knew before posting the question (see http://blog.stackoverflow.com/2011/07/its-ok-to-ask-and-answer-your-own-questions/). However, I'd be opposed to doing it on MO except in fairly unusual circumstances. In particular, MO should not be for advertising your own results (asking "Can one prove X?" and then answering it "Why, yes, it follows from my latest theorem.") or even for advertising wonderful folklore or results from other people's papers. I agree with Ryan is that the whole reason MO works the way it does is because it involves questions people genuinely want answered. Communicating things you think other people would or should like to know is also important, but very different and suitable for another site.
Good mathematics begets good questions. If you have a piece of nice mathematics you want to share, then identify a good question which stems from it, and write a MathOverflow post asking that question.
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