Fundamentally, they both live on the big three - heat, wave and Laplace equations. They both carry that trilogy of toolbox in an attempt to approximate the real world for practical benefits, which real world is a complex dynamical system. The pursuit of engineers allows better approximation. Consequently, engineers may seem more authentic. However, the two are cousins. Here is the tragedy, the two hardly talk. The world would be a better place if they talked more often.