This presentation examines the tenuous link between advances in applied mathematics and translating those advances into real value, as well as the culture clash between mathematics and engineering. Using nonlinear optimization as an example, several barriers that prevent theorems from translating into practical value are described. To overcome this cultural divide, it often takes a mathematically-minded engineer or engineering-minded mathematician, a so-called "mingineer," to translate between the two disciplines. Notions like "optimality," "numerical noise," "asymptotics" and "elegance" have completely different meanings in the two contexts. These barriers are illustrated using case studies from chip design and energy analytics. Best practices for achieving successful application of mathematics to solve practical engineering problems will be discussed in the context of these case studies.