Ph.D. in engineering after Ph.D. in mathematics
From what I know, it would hurt you. From the MIT ECE website (just as an example):

If I already have a PhD, can I apply for another PhD in EECS?
No, we will not admit an applicant who already holds a PhD degree (even if it is in a different area such as Physics or Math).

I'm sure it's like this at many of the top schools in the US. Here I'm assuming what you refer to as a &quot;doctoral degree&quot; will be treated the same way as the American/English &quot;Ph.D.&quot;