סמינר מחקר 17 לאפריל: Juan Luis Gastaldi (ETH Zurich) - The Language of Mathematics: Epistemological Consequences of Applying AI Methods to Mathematics

Juan Luis Gastaldi

ETH Zurich

The Language of Mathematics:
Epistemological Consequences of Applying AI Methods to Mathematics

Recent years have seen a remarkable development of deep neural network techniques for data analysis, along with their increasing application in scientific research across different disciplines, including mathematics. In this presentation, I intend to provide insight into the epistemological consequences of this novel research orientation. My main claim is that although current AI applications in mathematics stand on different and sometimes diverging implicit assumptions concerning the nature of mathematical knowledge and objects, they all share the use of tools and models resulting from natural language processing (NLP), forcing us to reflect on the implications of a distributional rather than analytic approach to the philosophy of mathematics. Accordingly, I will propose specific non-neural distributional methods to extract symbolic principles underlying textual corpora suitable for the characterization of mathematical objects, indicating the challenges and orientations that can be drawn for a data-driven philosophy of mathematics.

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