Language acquisition is a computational process by which linguistic experience is integrated into the learner’s initial stage of knowledge. To understand language acquisition thus requires precise statements about these components and their interplay, stepping beyond the philosophical and methodological disputes such as the generative vs. usage-based approaches. This study reviews several mathematical models that have guided the study of child language acquisition: How learners integrate experience with their prior knowledge of linguistic structures, How researchers assess the progress of language acquisition with rigor and clarity, and How children form the rules of language even in the face of exceptions. The study suggests that these models are applicable to second language acquisition (L2), yielding potentially important insights on the continuities and differences between child and adult language.