Why do engineering PhD programs require undergrad degrees in engineering or physics? I notice that many top American engineering PhD programs ask for undergrad or master degrees in engineering or physics, but this discussion excludes math majors.  How come?  Are math majors not qualified because the training is vastly different from engineering?

I'm a math nerd interested in applications-oriented maths, but many of these research questions are worked on in engineering depts.
I'd expect many math majors to have the skills needed to succeed in an engineering program, but they are likely to lack the vocabulary needed.  This is especially true if the engineering is theoretical or computational.  

I would not be surprised if math majors are accepted from time to time.