Should MU be a knowledge base for all mathematics?

Question

I, for one, think that MU should try to be a Q&A site that is accessible to people at a lower level than MO. This does not mean that it should be a lower quality site than MO. It's been suggested that MU should be an all-encompassing knowledge-base of mathematics, but this is an impossible goal, and I think that aiming for it will damage the quality of the site.

If stricter rules are not put in place, this community will founder. I realize that some of you dislike MathOverflow because it is full of "elitists and snobs", but you have things to learn from them.

Discuss

Answer 1

"For any reasonable query to Google asking about some question in Mathematics, I want a question on MU which answers it (barring trivial calculations, of course)."

This is impossible. Or at the very least, simply begs the question of what "reasonable" and "trivial" are to mean for us.

I see what this site could most usefully try to become as two main things. One is a repository and Q&A site for people to come to when they have done some work to research their question elsewhere and not been satisfied with the response. Harry has mentioned elsewhere that a lot of the sub-research level sites for math questions suck. As a first pass at a goal, then, I'd like MU to be a place where people can come for quality answers to sub-research level questions. I think it will be helped in this, compared to an arbitrary math help site, by an interested and invested community of users, and the SE platform itself, in which it is harder for questions to get lost than it is in a forum, and the quality of answers can be indicated in some rough way.

Question-answerers need help in creating quality answers from the askers, who need to have thought carefully about exactly what to ask, and perhaps indicated that they've searched around a bit before asking here. If I can write you an answer based on one search query, forget it.

The question then arises, if these aren't research level questions, why bother answering? Why not just link somewhere with the answer for the majority of questions?

One thing I love about MO, and a major reason I think it is useful and thriving in the research mathematics world, is that answers frequently give nuanced accounts of how the answerer thinks about the concept or problem at hand. It's more than you can get from a textbook much of the time, even when the answer to the question is known, and it gives you your pick of interpretations. Lurking behind most MO questions is something the asker has thought about but doesn't understand as well as they want to, and expert human answerers can give responses that not only clarify confusion and are correct mathematics, but give their own experience of coming to an understanding of the answer, which is invaluable. With a community of experts and good questions, people get answers to questions they couldn't think to ask explicitly. The answers on MO are more exploratory than is typical on math question sites, and they give the sense, often, of asker and answerers puzzling over the thing together. This could be seen as a corollary of the questions being research-level, but I think it is more fundamental to the philosophy and concept of the MO community than that, and it is something worth striving for here.

That's where I see MU's usefulness for questions like "What is an inner product space?" Answers can and should go beyond the technically sufficient response--a definition--to a coherent and motivated account of the concept (that doesn't stray too far away from the question, of course).

I mentioned two main things--the other one is a truly MO-like site for undergraduate-level (liberally defined) mathematics questions. Essentially, questions that are not actually research-level, but "feel like" research questions to the undergraduate asker--questions that are not routinely explained in the curriculum, or which the asker feels like he does not have the tools to answer as a straightforward extension of his current knowledge.

Answer 2

The idea of this beta phase is exactly to define what questions are good, and which aren't. We can talk about this theoretically here, but IMO the best way to go about it is to just post as many questions as possible, and on a case by case basis close the ones which seem out-of-place. That's the easiest way to define what this community does include, and is the exact reason we're having this beta phase.

This, by the way, is the reason I support asking even stupid questions: it lets the community set up practical guidelines on a case by case basis, which is better than trying to decide theoretically what kinds of questions we allow.

To answer your actual question though, yes, I think this site should encompass all Math knowledge (below the research level). For any reasonable query to Google asking about some question in Mathematics, I want a question on MU which answers it (barring trivial calculations, of course). But again, it's more practical to decide this on a case by case basis.