>>11668234>more recently he was wanting to go towards more research based jobs. So two years ago he got his PhD and founded a consulting firm and is making way more than he used toNo, but the problem here is that ME research has basis for what's going on in the industry, and you can be immersed in research culture and get good recommendations based on industry research labs and voices that matter to people in ME PhD admissions committees.
Math is a different story because it is best studied in university, its primary research culture is in university, and there's an extremely high chance that you don't have the prerequisite courses / material. ME goes through a small amount of math - calculus, basic linear, etc., just to make the physics work out - and doesn't have the background for math without serious remedial courses in abstract algebra, analysis, combinatorics, topology, etc..
So yes, by all means do a PhD in ME afterwards, but you'll be met with a fuckton of opposition on the PhD side for mathematics.