In this short paper, we summarize (without proofs) the constructive method to approximate functions in the uniform (i.e. maximal error) norm, that was recently developed by the authors.This is in contrast to other methods (e.g. back-propagation) that approximate only in the average error norm. We comment on the novelty of the approach and possible extensions. The method includes a gradient descent method in the maximal error norm (i.e. a non-differentiable function) and a method to constructively add neurons "on the fly" to overcome the problem of local minima in the uniform norm.