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This year’s Nobel prize in physics has been awarded partly in response to the recent theoretical and experimental advances in topological states of matter. I review the conceptual development from Thouless’ formulation of a topological invariant to the 3D topological insulator, in which the study of various seemingly unrelated problems, such as the helium-3 superfluid, semiconductor spintronics, and graphene, have all played significant roles.

How Phase of Matter Got Associated with Topology