Mathematicians disagree on the essential structure of the complex numbers (2024)
Summary
The essay surveys four perspectives on the essential structure of the complex numbers—analytic, smooth, rigid, and algebraic—and argues that they are inequivalent yet each meaningful for different purposes. It discusses automorphism groups, interpretability between structures, and the role of set-theoretic constructions in making i and -i indiscernible, ultimately advocating that multiple conceptions are legitimate and informative for structuralist philosophy.