Explore optimal learning from data in this 53-minute lecture by Ronald DeVore at the Hausdorff Center for Mathematics. Delve into the challenge of constructing approximations from functional observations of unknown functions. Examine quantitative theory, error measurement, and model class information. Discover methods for determining the smallest possible recovery error and constructing near-optimal discrete optimization problems. Investigate variants involving noisy data and explore joint research findings. Cover topics including the learning problem, mathematical questions, quantified performance, point evaluations, stochastic settings, deep learning, and bridging gaps in numerical approaches.