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Math-aware fine-grain search is expected to be widely available. A key question is what roles it can play in mathematics. It will be argued that, besides finding information, math search can help advance and manage mathematical knowledge. This paper will present the short-term goals and state of the art of math-aware fine-grain search. Afterwards, it will focus on how math search can help advance and manage mathematical knowledge, and discuss what needs to be done to fulfill those roles, emphasizing two key components. The first is similarity search, and how it applies to (1) discovering and drawing upon connections between different fields, and (2) proof development. The second is math metadata, which math search will surely encourage and benefit from, and which will be pivotal to mathematical knowledge management.