Abstract

Abstract Saunders Mac Lane heard David Hilbert’s weekly lectures on philosophy and utterly believed Hilbert’s declaration that mathematics will know no limits. He studied algebra with Emmy Noether, and both mathematics and philosophy with Hermann Weyl. As a young algebraist he created today’s standard working method for mathematical structure: category theory, with topologist Samuel Eilenberg. As one step, they created the now standard definition of “isomorphism.” They originally saw categories as just a working tool. But in the 1950s, Mac Lane saw Alexander Grothendieck and others radically extend the range of the theory, and in the 1960s, he took up William Lawvere’s idea of categorical foundations. The essay relates all of this to current philosophical structuralism, especially concerning isomorphisms and automorphisms of structures. It concludes by comparing Mac Lane’s motives for structuralist working mathematics with current philosophical motives for structuralist ontology.

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