What Is Research?

May 28, 2010

Planetmath and Mathworld losing out to Wikipedia

Filed under: Web structure,Wikipedia,Wikis — vipulnaik @ 10:59 pm
Tags: ,

As I’ve mentioned earlier (such as here), it has seemed to me for some time that both Planetmath and Mathworld are losing out as Internet-based mathematical references to Wikipedia. I don’t expect that there has been absolute decline in the traffic to these websites — the growth of the Internet by leaps and bounds would mean that a website has to make a fairly active effort to lose users. But I do expect that more and more of the new users who are coming in are treating Wikipedia more as a first source of information.

From the preliminary results of a recent SurveyMonkey survey: out of 29 respondents (most of them people pursuing or qualified in mathematics), 24 claimed to have used Wikipedia often, and the remaining 5 to have used it occasionally for mathematical reference information. For Planetmath, 22 people claimed to have used it occasionally, and 7 to have heard of it but not used it. For Mathworld, 5 people claimed to have used it often, 16 to have used it occasionally, 7 to have heard of it but not used it, and 1 to have never heard of it.

In response to a question on how Planetmath and Mathworld compare with Wikipedia, the nine free responses were:

  • Planetmath now loads too slowly, so I seldom use it. Even when I did use it often, I found that the articles tended either to be too incomplete, or too tailored to people who are already experts. Many Mathworld pages are still much better than many Wikipedia pages, but Wikipedia is more comprehensive.

  • planet math is slow!!! mathworld has more graphics and less maths.

  • Material is generally better presented on Mathworld, but the topics are more limited.

  • Not as much information as Wikipedia and not as well arranged

  • I usually find Wikipedia to be my first source and only go to Mathworld or Planetmath if wikipedia fails me. I guess that means Wikipedia is better.

  • Planetmath is dying, Mathworld is static.

  • I find wikipedia much more useful than Mathworld. Mathworld’s pages are very technical, which is not what I am looking for on the internet usually. Usually I am looking for someone’s nice conceptual understanding of a topic or definition (through nice examples), and Wikipedia usually has lots of these.

  • Planetmath is quite useful to find proofs. Mathworld is very specialised, but it has a few nice bits of information sometimes. They seem to both be quite stagnant compared to Wikipedia.

  • They can’t keep up. There was probably a time when PlanetMath was a better reference than Wikipedia, but it’s fading fast. I think their ownership model isn’t conducive to long term quality.

(See the responses to these and other questions here and take the survey here).

The general consensus does seem to confirm my suspicions. Why is Wikipedia gaining? Here are the broad classes of explanations:

  1. It’s just a self-reinforcing process. The more people hear about and link to Wikipedia, the more people are likely to read it, the more people are likely to edit it and improve it. But if that’s the case, why did Wikipedia ever get ahead of Mathworld and Planetmath? Two reasons: (i) its more radically open editing rules (ii) Wikipedia covers many areas other than mathematics, so people come to the site more in general. Also, since it covers many areas other than mathematics, it can better cover content straddling mathematics and other areas, such as biographies of mathematicians, and historical information that is relevant to mathematics. This creates a larger, strongly internally linked, repository of information.

  2. Planetmath’s owner-centric model (as mentioned in one of the responses) where each entry is owned by one person, does not create a conducive environment for the gradual growth and improvement of entries.

  3. The appearance of content is better on Wikipedia. Prettier symbols, faster loading, better internal links, better search. This is definitely an advantage over Planetmath, which has slow load times in the experience of many users (as indicated by the comments above) though perhaps not so much over Mathworld.

  4. Google weights Wikipedia higher (because of the larger size of the website and the fact that a lot of people link to Wikipedia). This is related to (1).

  5. The people in charge of Mathworld and Planetmath simply lost interest. Mathworld is largely run by Eric Weisstein, an employee at Wolfram, who seems to have recently been trying to integrate metadata about mathematical theorems and conjectures into Wolfram Alpha. Developing Mathworld continually to a point of excellence does not seem to have been a top priorty for Weisstein or his employer Wolfram Research (that hosts Mathworld) over the last few years. The people running Planetmath also may have become less interested in continually innovating.

Given all this, is Wikipedia the best in terms of: (i) the current product or (ii) the process of arriving at the product? While I’m far from a Wikipedia evangelist, I think that the answer to (ii) is roughly yes if you’re thinking of broad appeal. Anything which beats Wikipedia will probably do so by being more narrowly focused, but it may then not be of much interest to people outside that domain. A host of many such different niche references may together beat out Wikipedia for people who care enough to learn about a multiplicity of references. For those who just want one reference website, Wikipedia will continue to be the place of choice in the near future (i.e., the next 3-4 years at least, in my opinion).

Currently, Wikipedia is an uneasy mix of precise technical information and motivational paragraphs. It makes little use of metadata to organize its information; on the other hand, it is easy to edit and join in. The mathematics entries cannot be radically changed in a way that would make them radically different in appearance from the articles on the rest of the site. This opens up many niche possibilities, some of which are being explored:

  1. Lab notebooks, where people store a bunch of thoughts about a topic, without attempts to organize them into something very coherent. Here, good metadata and tagging conventions could allow these random lab notebook-type jottings to cohere into an easily accessible reference. This would be the mathematical version of open notebook science, a practice that is slowly spreading in some of the experimental sciences. nLab (the n-category lab) is one example of a “lab notebook” in the mathematical context. This is great for motivation, and also for understanding the minds of mathematicians and the process of mathematical reasoning.

  2. Something that focuses on a particular aspect of mathematical activity. For instance, Tricki, called the Tricks Wiki, focuses on tricks. Other references may focus on formulas, others may focus on counterexamples, yet others (such as the AIMath wiki on localization techniques and equivariant cohomology) may focus simply on providing extensive bibliographies. Somewhat more developed examples include the Dispersive Wiki and complexity zoo (actually, a computer science topic, but similar in nature to a lot of mathematics). Some may focus on exotic tricks of relevance to a particular mathematical discipline. There is some cross-over with lab notebooks, as the tricks become more and more exotic and the writing becomes more and more spontaneous and less subject to organization into an article.

  3. Highly structured content rich in metadata that is intended to provide definitions, proofs and clarify analogies/relations. Examples include the Group Properties Wiki [DISCLOSURE: I started it and am the primary contributor] which concentrates on group theory. The flip side is that the high degree of organization uses subject-specific structures and hence must be concentrated on a particular narrow subject.

There are probably many other niches waiting to be filled. And there may also be close susbstitutes for reference sites that weren’t created as references. For instance, Math Overflow, though not a reference site, may play the role of a reference site once it accumulates a huge number of questions and answers and adopts better search and specific tagging capabilities. Similarly, thirty years from now, the contents of Terry Tao’s weblog may contain a bit on virtually every mathematical topic, in the same way as Marginal Revolution have a bit on almost all basic economic topics (I say “thirty years” because economics is in many ways a smaller subject than mathematics).



  1. You seem to have buried the actually important reasons under 1, “just a self-reinforcing process”. 😛 Were you intentionally trying to discount them?
    Because I think that being more open to editing, easier to edit, having more incentives, and offering opportunities for several kinds of activities (writing, improving, tidying, deleting, quarrelling, etc.) have all been crucial to Wikipedia’s growth.

    Also, as a visitor, I know that when there is a Wikipedia page, if it is not satisfactory, I can usually find links at the end to Planetmath and Mathworld, while the others are dead ends. (Relative to Wikipedia, they are also dead ends when it come to exploring other topics.)

    Comment by S — May 29, 2010 @ 4:10 am

  2. Nice point. Yes, (1) was an umbrella point covering a lot of things. But my focus in (1) was that it was the self-reinforcement arising from a small initial difference in policy that mattered.

    Your point about the Wikipedia article being more “portal-like” in the sense of providing links to other articles when they’re better is certainly important. I should not have missed it.

    Also: While you may differ on this, I don’t think that Wikipedia’s mathematics entries are undergoing constant improvement in any significant way. Most of them are fairly stable with time, and the point at which they attain stability doesn’t seem to be the point at which they become really great. There is probably some sort of equilibrium attained where further improvements in the individual article would conflict with the general guidelines for writing Wikipedia articles.

    Comment by vipulnaik — May 29, 2010 @ 1:03 pm

  3. It is true that articles on Wikipedia do not constantly improve — once they “get written” essentially, they hover around some equilibrium (with decline in quality always being more likely than improvement). But the overall coverage is mostly improving, with new articles being created faster than old ones are deleted. This makes the website more valuable as a whole, and influences people’s impressions and decisions of which one they want to visit.

    Comment by S — May 30, 2010 @ 4:43 am

  4. I think we agree. Let’s agree to agree :).

    Comment by vipulnaik — May 30, 2010 @ 1:12 pm

  5. I didn’t even know that there was a question of disagreement. 🙂

    Another thing to point out: this question is probably best considered as two separate (not independent) parts:
    (1) why people are visiting Wikipedia more (it is getting better, it comes higher in Google), and
    (2) why [the answers to (1)] are happening (more fun to edit / wider scope, more people link to it).
    But there’s perhaps nothing new to be gained by looking at it separately. 🙂

    Comment by S — May 30, 2010 @ 9:14 pm

  6. You’re right — there are these two separate parts. And I think people often conflate the two, believing that any answer to (1) must necessarily involve (2), so that in order to achieve the results for (1) it is necessary to follow Wikipedia’s path on the answers to (2).

    In contrast, I think it’s possible that the answers to (1) (which may have to do with the nature and organization of content on Wikipedia) could well be achieved on smaller scales and within more narrow niches through methods completely different from those that Wikipedia has used.

    Comment by vipulnaik — June 3, 2010 @ 9:53 pm

  7. As one of the people running PlanetMath, I disagree with
    statement 5, although I see how the current state of the
    site could give that impression. We have never lost interest
    in the project or given up on innovating — rather the problem
    is one of lack of funds. Without adequate financial resources
    to hire programmers, system administrators, and other staff, it
    is simply impossible to maintain such a website properly or
    to carry our innovative ideas, of which there is no shortage,
    into practice.

    While Wikipedia is now a multi-million dollar operation, the
    total budget of PlanetMath has never been more than about $10000.
    With that sort of money, one can’t do much more than pay for
    domain registration, rent some server space, and occasionally
    make small contracts for piecework. Most of our labor has been
    provided on a volunteer basis by people with other commitments.
    Occasionally, we get a student as an intern or working on part
    of our codebase as an academic project. While such help has
    done a lot to advance PlanetMath, it also only comes sproadically
    and isn’t enough by itself.

    This meagre financial situation also explains many of the other
    points which were raised. Without the money to buy servers or hire a
    system administrator, we are stuck with a slow, not too reliable
    system. Since things like nice graphics and user friendly interface
    take a lot of work to create, they are currently out of our reach
    and hence we have to make do with the same look and feel as when the
    site first opened a decade ago.

    Comment by Raymond Puzio — August 5, 2010 @ 7:56 pm

  8. Hola! I’ve been reading your web site for a long time now and finally got the courage to go ahead and give you a shout out from Houston Texas! Just wanted to tell you keep up the great job!

    Comment by kliknij — May 7, 2013 @ 9:37 am

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