The term “forgetting” appears throughout the materials artificial intelligence literature in multiple, often contradictory senses: as a catastrophic failure that destroys previously acquired knowledge of structure–property relations, as an unexamined side effect of data deletion or replay buffer limits, and occasionally as an implicit consequence of model capacity constraints. This conceptual ambiguity impedes precise communication, obscures design decisions, and prevents the field from treating forgetting as a controllable parameter rather than an inevitable defect. The present boundary/definitional paper proposes a precise definition of algorithmic forgetting as a deliberate design choice, distinct from both catastrophic forgetting and passive capacity limits. It distinguishes algorithmic forgetting from five nearby concepts—catastrophic forgetting, data deletion, privacy preservation, capacity saturation, and regularization-induced compression—by clarifying intent, mechanism, epistemic consequences, and reversibility. The paper further articulates the conditions under which forgetting becomes beneficial (adaptation to distribution shift in experimental data streams, selective retention under resource constraints, and controlled deletion for intellectual property or safety) versus harmful (loss of rare but physically valid examples). Finally, it supplies a materials-specific conceptual framework for deciding what to forget and what to retain, grounded in rarity, recency of validation, and relevance to the current search space. By reframing forgetting as an explicit design lever, this analysis offers materials AI practitioners a shared vocabulary and a systematic approach to engineering memory policies that enhance rather than undermine long-term scientific utility.