Can concepts from the theory of neural computation contribute to formal theories of the mind? Recent research has explored the implications of one principle of neural computation, optimization, for the theory of grammar. Optimization over symbolic linguistic structures provides the core of a new grammatical architecture, optimality theory. The proposition that grammaticality equals optimality sheds light on a wide range of phenomena, from the gulf between production and comprehension in child language, to language learnability, to the fundamental questions of linguistic theory : What is it that the grammars of all languages share, and how may they differ?