How does the Brain give rise to the Mind? How do neurons and synapses, molecules and genes, ​​evolution and development, give rise to behavior and cognition, language and intelligence? Despite lightning progress in recording and molecular technology and a deluge of experimental data, we do not seem to get closer to an answer. This is a talk about admiring and appreciating the problem, and proposing a new approach based on a recognized but little studied intermediate level of Brain computation carried out by the synchronous firing of large and highly interconnected sets of neurons called assemblies. We show that assemblies give rise to a novel computational system, and we speculate that they may instrument higher cognitive functions, such as language and math.