Unknowable Truths: The Incompleteness Theorems and Modernism
Sciences and Mathematics, College of
Math and Computer Science, Department of
BURS Faculty Advisor
This article evaluates the function of the current history of mathematics methodologies and explores ways in which historiographical methodologies could be successfully implemented in the field. Traditional approaches to the history of mathematics often lack either an accurate portrayal of the social and cultural influences of the time, or they lack an effective usage of mathematics discussed. This paper applies a holistic methodology in a case study of Kurt Gödel’s influential work in logic during the Interwar period and the parallel rise of intellectual modernism. In doing so, the proofs for Gödel’s Completeness and Incompleteness theorems will be discussed as well as Gödel’s philosophical interests and influences of the time. To explore the intersection of these worlds, practices are borrowed from the fields of intellectual history and history of science and technology to analyze better the effects of society and culture on the mind of mathematicians like Gödel and their work.
Tvardy, Caroline, "Unknowable Truths: The Incompleteness Theorems and Modernism" (2020). Belmont University Research Symposium (BURS). 85.