Members' Colloquium

Although Lewis Hyde's The Gift is primarily concerned with the status of works of art, he does devote part of a chapter to arguing that scientific research functions as a gift economy: the scientist (ideally) contributes new knowledge as a shared resource for the community, which in turn is built on this sharing. Hyde doesn't specifically refer to mathematics, whose community in many ways exemplifies this ideal. Framed in this way, the crucial distinction is not between human and machine mathematics, but rather between human and corporate mathematics, and this latter distinction is responsible for the "severe misalignment," identified in a letter signed by 25 Fields medalists, between the announcements of the AI industry and the practice of human mathematics. I will explore what it means to view the former as a gift economy, and ask how AI-generated mathematics can be integrated into the gift economy under conditions of what Terence Tao has called "proof abundance."