In recent years, Machine Learning has emerged as a promising avenue for sourcing numerical methods in partial differential equations. This resulting field of scientific/mathematical machine learning has made swift progress in reproducing physically plausible solutions to canonical problems in PDE numerics. This talk will cover background to overview this research thread and some topical results before considering two prevalent PDE learning problems in forecasting and physics. We will then present some geometry and probability arguments for essential numerical analysis in these baseline solutions and examine further solution implications.