Language and Mathematics in the Time of AI. Philosophical and Theoretical Perspectives

By Juan Luis Gastaldi — ETH Zurich Under the banner of Artificial Intelligence (AI), the past decade has witnessed a remarkable development of deep neural network techniques for data analysis, along with their increasing application across scientific disciplines, including mathematics. In this presentation, I will explore the philosophical implications of these developments and argue that they may yield new theoretical insights into the nature of mathematics. The path from philosophical to theoretical insights will be guided by the claim that, owing to the relative success of neural methods, natural language has become central to the computational treatment of mathematical content, forcing us to reflect on the implications of a distributional rather than an analytic approach to mathematics. After providing philosophical, historical, and epistemological perspectives on this problem, I will conclude by proposing some conceptual orientations for a distributional approach to mathematical contents, in line with ongoing theoretical efforts to develop a formal framework for extracting symbolic principles underlying textual corpora.