Abstract Summary
In 1932, Professor Cassius Jackson Keyser called for “the disciplining of men, women, and children in the art of ‘postulate detection.’” An essential goal of education, he believed, was to teach Americans how to find the hidden assumptions that determine every system of thought, from politics to religion to philosophy. As Adrian Professor of Mathematics at Columbia University, Keyser had spent part of his career studying the foundational assumptions, or axioms, at the heart of mathematical reasoning. While the axioms of mathematics had traditionally been regarded as “self-evident” truths, mathematicians around the turn of the twentieth century became wary of such claims and began to distinguish between “axioms” and “postulates.” Unrelated to self-evidence or truth, postulates were simply agreed-upon statements used to construct a system of reasoning. For Keyser and other American mathematicians, postulate sets became their own field of mathematical interest tied to contemporary considerations of rigor. In this talk, I discuss how the study of postulates and their properties—like consistency (no postulate contradicts another) and independence (no postulate can be derived from another)— was used to criticize the abstract, out-of-touch practices of modern mathematical research as well as to celebrate its artistry and virtues. Overall, I situate what would later be referred to as “American Postulate Theory” within the landscape of modern mathematics as well as the early- twentieth-century growth of the American mathematics community.
