Wolfram Computation Meets Knowledge

A New Look and New Features for MathWorld

While MathWorld continues to be the most popular and most visited mathematics site on the internet, and while its mathematical content continues to steadily grow and expand, MathWorld readers will today notice more immediate visual changes.

Design changes and major new pieces of functionality are generally years in the making for large informational websites like MathWorld. The last time the site received a major infrastructure upgrade was in July of 2005 (see “MathWorld Introduces New Interactive Features for Teachers and Students,” MathWorld headline news, July 6, 2005).

On February 8, we introduced a major update of the MathWorld site featuring improved navigation, higher-quality typesetting and links to interactive Demonstrations.

The new features introduced on MathWorld include:

  • New streamlined “platformed” look and feel
  • New interactive Demonstration collections and links
  • Improved mathematical typesetting
  • Collapsible navigation link trails
  • More-prominent ways to contribute to MathWorld

Each of these elements is described in more detail below.


Platformed page for Sphere

MathWorld is the second Wolfram Web Resource (following the Wolfram Demonstrations Project—about which you’ll hear much more below) to become “platformed.” Platforming is a graphical design in which different functional components are broken off into delineated regions, each with its own frame or border. This makes it possible to visually identify the relevant parts of a web page for easy reading and navigation. In the case of MathWorld, the main visual elements are enclosed in framed, shadowed boxes with a green stripe at the top. An example of the way this works is shown above for the Sphere entry. Most readers find that this new layout greatly improves readability. I hope you do as well.

Interactive Demonstrations

A very nice element of the new design is extensive interlinking with the Wolfram Demonstrations Project, an open-code, Mathematica-powered resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance and many other fields. (Perhaps chief among these, however, is mathematics.)

Like MathWorld, the contents of the Demonstrations Project grow daily thanks to readers and Mathematica users from around the world who participate by contributing innovative Demonstrations. As of this writing, the Demonstrations Project contains a total of 2404 individual Demonstrations.

MathWorld left sidebar

When a given MathWorld entry has related Demonstrations, they are displayed in the right column of that entry, as illustrated below. These are constantly being updated as new Demonstrations are added. A complete list of all MathWorld pages containing Demonstrations links is also available by clicking the left sidebar’s “Interactive Entries” link. That number already exceeds 1000, with many more to be added in the upcoming weeks and months.

DOWNLOAD Mathematica Notebook

Mathematica notebooks used in the computations and visualizations appearing on MathWorld have been downloadable for many years by clicking the small icon illustrated above at left that appears on several thousand of MathWorld’s pages. These notebooks are fully evaluatable in Mathematica, and were viewable in static form by anyone who downloaded the free MathReader program. Interactive Demonstrations

With the release of Mathematica 6 last May (see “Mathematica 6 and the Wolfram Demonstrations Project Launched,” MathWorld headline news, May 3, 2007), MathReader was replaced by the much more powerful Mathematica Player.

Like its predecessor, the free Player allows static Mathematica notebooks to be viewed by everyone, including those without access to the full Mathematica itself. Unlike MathReader, Player also allows interactive Mathematica content and graphics to be viewed and manipulated. To aid users in viewing both MathWorld and Demonstrations notebooks, the first time you click on a notebook icon in MathWorld, you are now presented with a popup window giving you the opportunity to download a copy of Player.

The Demonstrations website is a very nice complement to MathWorld, and the sites are now extensively cross-linked. So please feel free to explore the mathematical concepts you read about on MathWorld in fully interactive form on the Demonstrations site.

Improved Typesetting

MathWorld has been authored and typeset in Mathematica since 2005 (see “MathWorld Introduces New Interactive Features for Teachers and Students,” MathWorld headline news, July 6, 2005; for additional details about how the authoring and website-generation process works, see my recent article in The Mathematica Journal).

The advent of Mathematica 6 has made a number of improvements possible, in particular the ability to antialias typeset mathematical formulas. As the comparison below shows, the new typesetting that now appears on MathWorld (bottom figure) courtesy of Mathematica 6 vastly improves the visual quality and readability of equations compared to the previous pixelated versions (top figure).

Old aliased equations

New antialiased equations

Collapsible Link Trails

In addition to containing a large amount of interlinked mathematical knowledge, MathWorld has always made it simple to locate that knowledge. As well as containing upwards of 130,000 cross-links, being fully text searchable, having a complete alphabetical index and sporting a classroom section for students and teachers, MathWorld also features an extensive subject-based link trail at the top of each entry. These links allow related concepts to be navigated in parallel, making it both easy and convenient to find other related material.

As regular MathWorld readers may have noticed, the sheer number of individual link trails could in some cases get in the way of just reading an article. This was particularly true in, for example, the case of articles about graph theory, where many different classifications of a given graph could pile up, obscuring the actual textual entry below. (Not so coincidentally, in addition to writing and maintaining MathWorld, I am also the developer for the mathematical curated data collection known as GraphData that is built in to Mathematica 6, where many of these classifications will look rather familiar.)


If you’re a reader of MathWorld, you probably already know the site as the world’s most visited mathematical resource. You may even have noted that MathWorld is updated with new and enhanced material on an almost daily basis. What you may not know is that your contributions are vital to the continued growth and high quality of the site. The attempt to create, maintain and keep MathWorld up to date is a truly monumental task. I couldn’t do it without the helpful comments and contributions that thousands of readers just like you have submitted over the years. Your comments are extremely valued and helpful, so please feel free to make liberal use of the “Contribute to MathWorld” and “Send a Message to the Team” links in the left sidebar of every entry. For your convenience, a new “Contact the MathWorld Team” link has also been added to the bottom of each page, as illustrated below.

Contact the MathWorld Team

In addition to contributing to MathWorld—be it in the form of an additional reference, extension to an existing entry, entirely new entry or any other suggestion—please also do consider writing and contributing your own interactive Demonstration. There are certainly many topics on MathWorld that are ripe subjects for Demonstrations. And not only is the new dynamic interactivity in Mathematica 6 (which makes this amazing degree of interactivity possible) easy to use and fun to program, but you can immediately share your knowledge and insight with a large audience of interested people in a fully interactive way. Readers of The Math behind NUMB3RS website, written by the Wolfram NUMB3RS team (which both myself and MathWorld associate Ed Pegg Jr are privileged to be a part of), have probably already noticed the extensive use of interactive Demonstrations to enhance and extend the reader experience. Together, MathWorld and the Demonstrations Project provide an extremely rich and growing framework for generating, collecting and disseminating mathematical knowledge. Which is, after all, what MathWorld is all about.