Exploration has always centered on claims: for country, for commerce, for character. Claims for useful scientific knowledge also grew out of exploration’s varied activities across space and time. The history of the Canadian Arctic Expedition of 1913–18 exposes the complicated process of claim-making. The expedition operated in and made claims on many spaces, both material and rhetorical, or, put differently, in several natural and discursive spaces. In making claims for science, the explorer-scientists navigated competing demands on their commitments and activities from their own predilections and from external forces. Incorporating Arctic spaces into the Canadian polity had become a high priority during the era when the CAE traversed the Arctic. Science through exploration—practices on the ground and especially through scientific and popular discourse—facilitated this integration. So, claiming space was something done on the ground, through professional literature, and within popular narratives—and not always for the same ends. The resulting narrative tensions reveal the messy material, political, and rhetorical spaces where humans do science. This article demonstrates how explorer-scientists claimed material and discursive spaces to establish and solidify their scientific authority. When the CAE claimed its spaces in nature, nation, and narrative, it refracted a reciprocal process whereby the demands of environment, state, and discourse also claimed the CAE.