Sanjeev and I discuss some of the progress toward understanding how deep learning works, specially under previous assumptions it wouldn't or shouldn't work as well as it does. Deep learning poses a challenge for mathematics, because its methods aren't rooted in mathematical theory and therefore are a "black box" for math to open. We discuss how Sanjeev thinks optimization, the common framework for thinking of how deep nets learn, is the wrong approach. Instead, a promising alternative focuses on the learning trajectories that occur as a result of different learning algorithms. We discuss two examples of his research to illustrate this: creating deep nets with infinitely large layers (and the networks still find solutions among the infinite possible solutions!), and massively increasing the learning rate during training (the opposite of accepted wisdom, and yet, again, the network finds solutions!). We also discuss his past focus on computational complexity and how he doesn't share the current neuroscience optimism comparing brains to deep nets.