Over a lifetime the brain performs hundreds of thousands of individual cognitive acts of a variety of kinds, including the formation of new associations and other kinds of learning. Each such act depends on past experience, and, in turn, can have long lasting effects on future behavior. It is difficult to reconcile such large scale capabilities quantitatively with the known resource constraints on cortex, such as low connectivity. Here we shall describe an approach to this problem, in terms of concrete functions, representations, and algorithms, that seeks to explain these phenomena in terms that are faithful to the basic quantitative resources available. Until recently an algorithmic understanding of cognition has been regarded as an overambitious goal for experimental neuroscience. As we shall explain, with current experimental techniques this view is no longer justified, and we should expect algorithmic theories to be experimentally testable, and tested. The opinions expressed in this video do not necessarily reflect the views of the Heidelberg Laureate Forum Foundation or any other person or associated institution involved in the making and distribution of the video.