It is immediately clear to anyone who has used the site that Wolfram|Alpha knows a lot about mathematics. When computing integrals, sums, statistics, properties of mathematical objects, or a myriad of other mathematical and mathematics-related problems, it typically returns an extensive and exhaustively complete result. Which is of course not surprising, given that Wolfram|Alpha has the entire power and knowledge of Mathematica behind it, especially when combined with the fact that this native “smarts” is further augmented with large amounts of curated data and customized processing.
However, many visitors to the site have noted in the past that Wolfram|Alpha had relatively little computable knowledge about mathematical terms themselves, a state of affairs in contrast to its knowledge of words in the English language, and perhaps surprising in light of the existence of another Wolfram site devoted to the definition and description of terms in mathematics, namely MathWorld.
As readers of MathWorld likely already know, the entire MathWorld website is written and built using Mathematica. It has therefore been possible to programmatically process the entire 13,000+ entries comprising MathWorld into the native data format of Wolfram|Alpha, thus exposing its content in more computable form.
As an example of the sort of new knowledge this confluence brings to Wolfram|Alpha, consider the input “Lorenz attractor”. In the past, this would simply bring up a Wolfram|Alpha future topic page.
With the incorporation of MathWorld content, the default parse now goes to a description of the attractor, complete with an illustrative figure and some helpful typeset equations:
There are typically two additional and useful buttons on the right side of the “Definition” pod: a button to further expand the definition excerpt (“More details”) and a direct link to the full MathWorld entry (“More information”).
In addition to the main definition portion of the result, there are two additional pods: “Related topics” (providing links to other related MathWorld terms in Wolfram|Alpha) and “Subject classifications” (providing links to terms having similar subject classifications):
In the former pod, related definitions are just a click away, while in the latter pod, the “Show details” button can be used to expand the subjects into their full MathWorld and Mathematics Subject Classification (MSC) forms:
Furthermore, clicking any of the subjects gives a list of all MathWorld definitions falling into that category; for example, in the case of “chaos”:
In the case of some terms of special interest in mathematics education, additional information is given when possible on educational grade level and standards, as illustrated in the parse for “acute angle”:
Again, clicking either the grade level or the name of the standard will return a list of all entries sharing that property, together with any appropriate illustrations:
Based on the feedback we’ve been receiving over the last months, the incorporation of this mathematical content into Wolfram|Alpha seems like something that will be useful to many visitors. There remains much work to be done. But, as you’d expect, these limitations are currently being worked on, so expect even smoother and more complete integration of the two sites moving forward. As always, your comments toward improving both are most welcome as this process continues.