Mathoverflow has led in several instances to new mathematical work that arose directly from mathematical ideas, questions or answers posted here. Articles containing such work, inspired in fundamental part by mathoverflow material, might be characterized as having been born on mathoverflow.

Let us collect together here references to such work. In each case, please include a link to the relevant mathoverflow post or posts, a link to the mathematical work, for example an article at the math arxiv or the relevant journal, and a very brief summary abstract. (More detailed abstracts would presumably be available for those following the links to the article.)

In order that this question will not become burdened with excessive posts, let's agree to the following principles:

1. Please makes posts here only about essentially completed articles, rather than works-in-progress.
2. Please make posts here only about articles whose main existence was inspired by mathoverflow, such as a case where the topic of a question or the essence of an answer became the main substance of an article.
3. Please do not make posts here concerning articles simply because they cite mathoverflow, or simply because mathoverflow was involved at a critical step of the article, since such citations will eventually become so numerous as to be unremarkable. Rather, make a post here only in connection with an article that could be characterized as essentially about the topic or ideas expressed on mathoverflow and the authors were directly inspired by that mathoverflow material.

Please also note that the related meta-thread is for more general discussion about references to mathoverflow, and Gower's question on breakthroughs that seeks examples of situations where mathoverflow helped a researcher make a critical advanceas part of a larger work.

Mathoverflow has led in several instances to new mathematical work that arose directly from mathematical ideas, questions or answers posted here. Articles containing such work, inspired in fundamental part by mathoverflow material, might be characterized as having been born on mathoverflow.

Let us collect together here references to such work. In each case, please include a link to the relevant mathoverflow post or posts, a link to the mathematical work, for example an article at the math arxiv or the relevant journal, and a very brief summary abstract. (More detailed abstracts would presumably be available for those following the links to the article.)

In order that this question will not become burdened with excessive posts, let's agree to the following principles:

1. Please makes posts here only about essentially completed articles, rather than works-in-progress.
2. Please make posts here only about articles whose main existence was inspired by mathoverflow, such as a case where the topic of a question or the essence of an answer become became the main substance of an article.
3. Please do not make posts here concerning articles simply because they cite mathoverflow, or simply because mathoverflow was involved at a critical step of the article, since such citations will eventually become so numerous as to be unremarkable. Rather, make a post here only in connection with an article that could be characterized as essentially about the topic or ideas expressed on mathoverflow and the authors were directly inspired by that mathoverflow material.

Please also note that the related meta-thread is for more general discussion about references to mathoverflow, and Gower's question on breakthroughs seeks examples of situations where mathoverflow helped a researcher make a critical advance as part of a larger work.

As MO declares itself as a site for "research level"

Mathoverflow has led in several instances to new mathematical workthat arose directly from mathematical ideas, questions and or answersI wonder how its actual impact posted here. Articles containing such work, inspired in fundamentalpart by mathoverflow material, might be characterized as havingbeen born on mathematical research ismathoverflow.

Let us collect together here references to such work. In view of numerous outstanding and inspiring answerseach case,I am pretty sure that many people gain please include a lot link to the relevant mathoverflow post or posts, alink to the mathematical work, for their research as individualsexample an article at the matharxiv or the relevant journal, and a very brief summary abstract.Moreover(More detailed abstracts would presumably be available for thosefollowing the links to the article.)

In order that this question will not become burdened with excessiveposts, it seems pretty clearlet's agree to the following principles:

Please also note that it would be nice the related meta-thread is for more general discussion about references to have them collected at some placemathoverflow, and Gower's question on breakthroughs seeks examples of situations where mathoverflow helped a researcher make a critical advance as part of a larger work.

As MO declares itself as a site for "research level" questions and answers I wonder how its actual impact on mathematical research is. In view of numerous outstanding and inspiring answers, I am pretty sure that many people gain a lot for their research as individuals. Moreover, it seems pretty clear, that MO has a great impact on the mathematical community as a whole (at least on the online part of it).

But did it happen that an MO question/answer dialog prompted actual collaboration, joint work/projects, or even joint papers? I am curious to hear your stories!

There is a related meta-thread and a related question by gowers and you'll already find some stories about MO-initiated joint papers there. However, I thinks there are more and that it would be nice to have them collected at some place.