That said, I strongly disagree with your disagreement. There was a recent paper whose abstract I read that made me think of homotopies between convolutional networks. Unfortunately I lost the paper behind some stream and never got to read it proper. In the context of that, I realized that the search for convnet design will likely soon be highly automatable, obsoleting much of the work that many DLers are doing now.
What will be future proof is understanding information theory so that loss functions become less magical. Information theory is needed to understand what aspects of the current approaches to Reinforcement learning are likely dead ends (typically to do with getting a good exploration strategy, also related to creativity). Concentration of measure is vital to understanding so many properties we find in optimization, dimensionality reduction and learning. Understanding learning stability and ideal properties of a learner/convergence means being comfortable with concepts like Jacobians and semi-positive definiteness for a start.
Probability theory is needed for the newer variational methods, whether in the context of autoencoders or a library like Edward (whose like I think is the future). Functionals and the variational calculus is becoming more important, in both deep learning and for understanding the brain. There's lots of work in game theory of dynamical systems (think evolutionary game theory) that can help contextualize GANs as a special case of a broader category of strategies.
Much to the contrary, the topics I mentioned are both the future of deep learning and future proof in general. This blog post by Ferenc captures my sentiment on the matter: http://www.inference.vc/deep-learning-is-easy/