Mathematical anxiety in the age of AI: Opacity, role inversion, and the changing place of the mathematician

Abstract

In the recent years, numerous mathematical discoveries were made due to AI-based technologies. Several recent reactions to such technologies have viewed them as a potential threat to mathematical practices, as inducing intimidation or even as causing destruction of mathematics itself. This paper argues that these reactions can be understood as expressing underlying anxiety, tracing this shift against earlier mechanization debates. Whereas older mathematical machines – from Leibniz's calculating machine to the Jevons' Logical Piano – prompted concrete fears while preserving the mathematician's role as locus of judgment and conceptual invention, contemporary AI-based technologies may induce anxiety resulting from an interlacement of three epistemic conditions: hermeneutical opacity, structural opacity, and role inversion. By examining AI-generated proofs and formalization, I show how a psychoanalytical lens can illuminate such AI-induced anxiety in mathematical research, framing these epistemic conditions as expressing a fundamental disorientation of the mathematician's place within AI-pervaded mathematical practices.