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There are some questions that deal with proofs that I'd say are pretty clearly computational science. For instance, the question The Lax-Milgram Lemma in FEM with non-homogenous Dirichlet BC seems like a computational science question.

Then, there are questions like the recent How to prove the 2-norm of an invertible matrix is exactly the reciprocal of its minimum singular value? that are usually flagged for closure.

Currently, the FAQ reads: "Mathematics, ask on math.stackexchange.com if it is oriented towards proofs and analytical calculation not of a numerical or computational character." The second question above falls into a little bit of a gray area.

What sort of distinction do we want to draw between mathematics questions that are appropriate for the site versus mathematics questions that should be migrated to Mathematics Stack Exchange? My first hack at this would be to say that "questions that do not demonstrate a clear connection to computational science should be migrated". The first question demonstrates a much clearer connection (it looks like a problem using finite element methods) to computational science than the second (which could be related to computational science -- it is linear algebra, after all -- or it could just be a math question).

My tendency is to be more permissive (we could stand to grow the site a bit). Simultaneously, this site is a community. We rely on the participation of high-reputation users in curating the site, and your input is very important in helping the site grow, so I'd like your opinion on moving forward. A decision on this issue should make it into the FAQ.

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I'm in favor of allowing applied math questions, including proof inquiries related to linear algebra, ode's & pde's, and optimization regardless of discernible ties to computational science.

That being said, there is no guarantee that our community will be able to answer all such proof based questions. If a question like this remains unanswered for too long, its a sign that it may be best migrated.

As ChristianClason points out, the 2nd question may be of low quality but remains on topic in my opinion.

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I'm also in favor of inclusivity -- both for the reason mentioned in the question, and because numerical and applied mathematics as a discipline tend to be given short shrift on Math.SE and (especially) MathOverflow. So I would be happy if (good) questions on these topics would be welcome here.

For me, migration (or suggesting to close and repost if there's no migration path) is for the benefit of the person asking ("Your question will likely not get a good answer here, but will over there"), not for preserving the "purity" of the site. (Computational science/scientific computing is a small and diverse enough community not to have to worry about losing participants by losing focus, I believe.)

That being said, your second question is not an ideal example here because it lacks both effort and context -- it would be closed pretty fast on most SE sites even if perfectly on-topic. Actually, I looked at some other questions migrated to Math.SE, and they all fall into the same pattern, which suggests to me that being off-topic is not really the problem here.

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  • $\begingroup$ I tend to migrate for similar reasons, and tend to err more on the side of giving an on-topic question time before migration. Post quality is another problem that should be discussed. Worth pointing out here is that low-quality posts are harder to migrate and more likely to cause us grief if we dump them on another site without contacting the destination site's moderators first. $\endgroup$
    – Geoff Oxberry
    Commented Jan 3, 2014 at 6:06

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