Data-driven materials discovery interpolates more reliably than it extrapolates and seldom reaches new structure types. We present MatEvolve, an agentic-AI framework designing crystals, proposing each candidate with a stated rationale and testing it. The agent reasons in an interpretable language of motifs, writing each crystal as a motif profile that describes the recurring geometric patterns—the motifs—composing it. The motif profile serves not merely as a description of a material but as the medium for material design: the agent edits the profile and constructs a crystal from the modified one, and the most promising candidates are validated by first-principles calculation. Applied to the design of rare-earth-lean permanent magnets, MatEvolve—built on the state-of-the-art language model Claude Fable 5 without fine-tuning—reaches new structural prototypes more than three times as often as generative models under an equal validation budget, at a comparable on-target-magnet rate. Beyond design, analysing the discovered crystals' human-readable profiles reveals structure–property relationships.