The original idea came from ActiveX, but it didn't take off until it was implemented across browsers via JavaScript as XMLHttpRequest over the next 6 years, and didn't become "Ajax" until the Adaptive Path blog post about Google's innovations with Maps and Gmail in 2005. Microsoft then added support for XMLHttpRequest a year and a half later in late 2006 with IE7, which of course had very little adoption, particular among businesses, because of IE6 (see IE6 @ 49.8% and IE7 @ 17.1% IE market share at beginning, March 2007, of this graph: http://www.w3counter.com/trends).
IE4 was the first browser with dynamic HTML (DHTML).
Microsoft evangelized the combination of DHTML, Javascript and ActiveX data controls to build applications similar to what we now call AJAX. Microsoft was ignored for various reasons.
Microsoft introduced XMLHttpRequest and evangelized DHTML, Javascript and XMLHttpRequest. They were ignored again.
It was not until the introduction of Gmail and Adaptive Path's coining of the term AJAX that people finally got it. By this time, Microsoft had already put IE on the back burner.