Humans and other animals can rapidly learn sequences of events and subsequently retrieve them with minimal repetition. By recording neuronal activity from four brain areas in human epilepsy patients performing a sequence learning task, we investigated how neuronal populations support this process. We examined two candidate sequencing algorithms, inspired by computer science: indexing and queuing. During learning, population activity occupied subspaces consistent with queuing and credit assignment. Once the sequence was fully learned, however, the overall neural geometry reorganized: the queue subspace became nonlinear, the enqueue subspace diminished, and the representation shifted toward an indexing-like format. Using network modeling, we further explored the governing principles underlying this transition, demonstrating that adaptive feedback control provides a plausible mechanism for the modulation of neural geometry during learning. Finally, we found that, upon successful learning, the hippocampus broadcasts sequence information to other regions through a low-dimensional subspace. Together, these findings suggest that sequence learning can be understood in terms of algorithmic neural subspaces and their dynamic reorganization across the course of learning.