Automating the math for decision-making under uncertainty

One reason deep learning exploded over the last decade was the availability of programming languages that could automate the math -- college-level calculus -- that is needed to train each new model. Neural networks are trained by tuning their parameters to try to maximize a score that can be rapidly calculated for training data. The equations used to adjust the parameters in each tuning step used to be derived painstakingly by hand. Deep learning platforms use a method called automatic differentiation to calculate the adjustments automatically. This allowed researchers to rapidly explore a huge space of models, and find the ones that really worked, without needing to know the underlying math.