The importance of math for machine learning didn't fully sink-in for me until I developed a deeper understanding of the back-propogation algorithm that makes tr

The importance of math for machine learning didn't fully sink-in for me until I developed a deeper understanding of the back-propogation algorithm that makes training deep neural networks computationally feasible. If it weren't for the introduction of a continuous activation function combined with the nice properties of the multivariate chain rule, we probably wouldn't be having this discussion at all. Another example that comes to mind is kernel methods used for Support Vector Machines. No matter where the inspiration for a model comes from, the final formulation is always mathematical, and I think that without an appreciation for the mathematics, it's hard to get a true feeling of a model's effectiveness and limitations.