It is beyond doubt that cognitive phenomena such as language and reasoning are the direct product of the activity of neurons and synapses. Making progress on this open question, often called the bridging problem, was identified by Richard Axel as the most important challenge in neuroscience today. The research community must identify, from among the ever growing volume of neuroscientific knowledge a conceptual core of basic elements and principles which may suffice for bringing about the brain’s function. Here we describe such a minimalistic model of the brain, and we demonstrate its power by implementing in it basic language acquisition. The mathematical neural model, or NEMO for short, is a simple realization of five basic ideas: excitatory neurons, brain areas, random synaptic connectivity, local inhibition, and Hebbian plasticity. We present algorithms showing the NEMO system is powerful enough to implement the essential rudiments of language acquisition: (a) learning semantic representations of nouns and verbs along with the part of speech for each word; and (b) learning the language's word order.