<p>The sky IS violet, it’s just that the convolution of the scattered spectrum and the response function of the eye peaks in the blue region of the visible spectrum!</p>
<p>Seriously though, physicists and mathematicians certainly can work as engineers, even with just an undergrad degree, provided that they take some care in their studies to appropriately prepare - a “typical” degree won’t do it, you have to take certain courses and maybe take part in some club activities. The distinction is that you will only be qualified in a few narrow specialties, whereas someone with an engineering degree has a much wider marketability - that is the trade off from all of those required engineering courses, they provide breadth that translates into mor ejob opportunities. Plus, engineering is inherently multi-disciplinary, so not having that broad background can really limit you to a role as a specialist.</p>
<p>Some sample match-ups:
Physics: Mechanical, Electrical (Antenna theory, device physics), Nuclear
Math: Aerospace, Electrical (signal processing)</p>