Is our mathematics natural? The case of equilibrium statistical mechanics

Abstract

Is human 20th-century mathematics a natural or an arbitrary logical construct? Some insight into this ill-posed but fascinating question is gained from the study of mathematical physics. A number of ideas introduced by physical rather than mathematical necessity turn out later to be mathematically useful. (Equilibrium statistical mechanics has been a particularly rich source of such ideas.) In view of this the author argues that our mathematics may be much more arbitrary than we usually like to think. © 1988 American Mathematical Society.