Being that I have an undergrad degree in engineering, and a PhD in mathematics I can share some light onto this topic. As an engineer, you are challenged with 'problem set' meaning there is a set of problems that require physics and or mathematics to determine the most correct solution. However, there are many limitations to this, one being as an engineer your job will evolve with new found solutions to theoretical physics or mathematics. Mainly, engineers 'apply' math and physics topics. Mathematicians, however consider a theory to be solved or proven wrong which utlimately leads to a scientific idea confirming one thing or diproving another. If the mathematical theory is valid, it can be tested to various applications and thus used as a tool for engineering. Example is Calculus the rigor proofs in both differential and integral calculus is a mathematical theory but the applications apply well to engineering. Sure, you may not need to understand the theory or relativity or even string theory to be an engineer. Nevetheless, theories hold the possibility of having great applications to the world we live in. For example, turbulence is a greatest unsolved problem for both physics and math, but if a theory is valid and proven the implications of such can change engineering forever. In the end as an engineer I felt limited and wanted to learn more and more about our world and try to understand from observations the great question of why? if your the same try learning more about mathematics, and physics.