>>11292965sure, typical approximations (e.g. FEM) work for routine applications of PDEs such as in aerodynamics and electronics, but any relevant advances go hand in hand with new points of view which can only happen by working directly on theory. mathematicians (or at least, very math-literate physicists) are behind all the flashy new techniques that keep appearing. anyhow, you're most likely a dumb undergrad without any experience in a firm that works with those models
