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Through it's younger PlanetMath is also quite a good reference for math, largely because it's maintained by the general public instead of a small team. Plus, all the content is distributed under the GNU FDL.

link

Of course, they'll need to use Conway's chained arrow notation just to get the sum down on paper.

Also, wikis in general are group authorship, although most don't aim to produce books. See the Portland Pattern Repository's WikiWikiWeb for an example.

Sure, It's nice that it's there, but to really learn math, you will need to take classes.
Mathworld is good for quick-reference definitions and theorem statements, but it's tough to learn from it.

If you're going to plug math content sites on Slashdot, though, you might as well plug PlanetMath, which in addition to being freely accessible, has all of its content published under the GNU Free Documentation License.

Don't get me wrong. Mathworld is a great resource. Eric did an enormous amount of great work putting it together. Unfortunately, being the work of a single person, it is and always will be limited in very important ways.

First off, all of the treasure troves always seemed very idiosyncratic. Since they represented only what the author felt was important / had access to / had time to write up, this was inevitable. Particularly amusing in the chemistry treasure trove which manages to be mostly useless to a college chemistry student while still bothering to include the mineral names of a great number of inorganic compounds.

The math treasure trove, by virtue of its sheer size, eventually escaped the worst effects of idiosyncrasy, but it still suffers from covering topics it varying levels of detail utterly out of proportion with their importance in mathematical study.

Despite all this, in its day, mathworld managed to be an enormously useful resource. However, even before it was shut down, it was beginning to totter under the effects of being (mostly) a one-man project. Despite the solicitation of "contributors," who did write a small fraction of the entries, Eric took a great deal of pride in having put the treasure trove together, and in his management of the treasure trove project, ensured that outside contributions would never be a substantial enough part of the project to threaten his claims to absolute control over it.

And absolute control was definitely one of his priorities. Mathworld was protected by some of the most stringent anti-mirroring measures I have seen. If the web server thought too large of fraction of the archive had gone to any IP or group of IP's, they banned the entire network. With a few rare exceptions, such bannings were without appeal. Yes, this meant that if someone else at your school attempted to mirror mathworld and got caught, you were banned from it until if and when your sysadmin managed to make nice with Eric.

I don't deny that Eric, being the author of almost all the material in the treasure-troves, had the right to do this. However, these policies forced me to reevaluate my opinion of him. Whereas before, I considered him a great altruist, I came to realize that offering mathword free to the public had no altruism in it at all -- it was simply a business decision to amass personal fame and publicity for his product, which he never intended to give to the public to use in any way he did not intend. Mathword, while originally free as in beer, was never free as in speech.

This is the great irony of mathworld's downfall: Because Eric never allowed anyone to have substantial collaberation in or to mirror the site, when it fell, the only way to get the information was off of a few illicit mirrors created from the CRC CD, and even then, Eric and Wolfram still shut down any mirror they became aware of. Again, I don't blame him for doing so -- it was his work. It just caused me to reevaluate the spirit in which the work was put together.

I now hold Eric Weisstein in about the same esteem as RMS. Both created a wonderful thing, but in time, their respective egos became one of the larger barriers to that thing acheiving its full potential.

What direction should mathworld have gone? What resources are there that attempt similar things in better manners?

First off, there is http://planetmath.org, a collaborative attempt at becoming what mathworld should have been. All contributions are under a public license of sorts, so it is immune to what befell mathworld. It is, however, still in its infancy. Go there, contribute, and fix that.

Second, there is http://www.mathforum.org, which has been bounced around from being a project of the Stanford math department, an independent dot-com, a subsidiary of WebCT, and now finally a not-for-profit sponsored by Drexel University. This is not an encyclopedia, it is a question and answer service for K-12 math questions. Because it is entirely volunteer-staffed, though, it actually answers whatever questions the volunteers feel like answering, and as a result, has amassed an archive of answers to math questions ranging from the most basic to graduate-level topics. In its current incarnation as a not-for-profit and with the site licnesed to print the authors' work with the author's retaining ownership, it should last as long as Drexel pays for the web space. I recommend that anyone who is interested volunteer as a Math Doctor to help enrich the site.

These two sites, I feel, far better embody the open-source spirit than mathworld, and in time their potential vastly exceeds anything Eric Weisstein will ever manage (mostly single handed). I bear no ill will towards Eric. I greatly respect his work. I just believe that the paradigm and motive it was compiled under are now obsolete, though it took the CRC morass to make me realize that.