Foundations of Mathematics I

Understand some important "crises" of intuition in the development of mathematical thought and the corresponding theoretical resolutions: the discovery of incommensurable magnitudes; the concept of infinity; the crisis of foundations and the axiomatizations of the late 19th century (geometries, continuum, set theory).

Critically analyze the main developments and the mathematical and philosophical implications of these topics through key examples from the history of mathematics, examining the responses provided by mathematicians to these crises

Students must be able to comprehensively present their knowledge, demonstrating critical ability in analyzing foundational issues, both in concrete examples and at a transversal level. Additionally, they must acquire communication skills, arguing their choices and presenting their knowledge with a good balance between precision in language and clarity in exposition.