Despite these recent successes at the neuroscience-AI intersection, there are many deep mathematical questions still to answer: 1) given their enormous size and complexity, how can we understand the operations performed by a fully-trained deep learning algorithm, or (analogously) an animal’s brain?; 2) how does the dynamics of activations within biological and artificial neural networks evolve and interact over different timescales (seconds, hours, days, etc.)?; 3) how does randomness in the environment and/or within the neuronal networks themselves contribute to the function of these networks?; 4) what features most enhance (or degrade) the computational power of neuronal networks?; 5) how do brains and AI systems reason in the face of uncertainty? This upcoming BIRS workshop will bring together AI researchers, neuroscientists, and mathematicians, to answer these questions. In so doing, it aims to advance all three of those disciplines, leading to better AI algorithms, and potentially better diagnosis and treatment of those with brain disorders.