The original article that seems to do the best to define the AJAX approach, is AJAX: A New Approach to Web Applications, by Jesse James Garrett, 18 February 2005. As subsequent interviews with him have indicated, Garrett popularized the name "AJAX" but disclaims having invented the term.

Garrett's article points out (in the lengthly 13 March 2005 Q&A that follows the main body of the piece) that "AJAX" is rather simpler than "Asynchronous JavaScript + CSS + DOM + XMLHttpRequest" to say and use. Garrett's success as a popularizer of the methodology is a direct outgrowth of his role as Director of User Experience Strategy at Adaptive Path, an organization of which he is a founder.

But perhaps the best indicator that a methodology has arrived is that there is a lengthy Wikipedia Explanation of AJAX (programming). This article includes some very valuable Pros & Cons about the methodology -- must reading!

The AJAX approach neatly circumvents some of the technical difficulties that always have been associated with Java Applets, which do [or attempt to do] roughly the same kind if thing, local processing of user data with minimum HTTP traffic unless it is absolutely necessary, but with modern GUI elements. The jury on which approach will dominate is still out, but a lot of smart money appears to be landing on the AJAX square.

Where this fits into issues of Web Application Quality should be clear. Java Applets are, as everyone knows, quite difficult to test because Applets are opaque and, as a result, somewhat less-than-perfect methods have to be used in creating regression tests for them. AJAX applications, on the other hand, are "pure browser" implementations, and as such they yield nicely to modern technologies.