Selected Topics in History and Philosophy of Mathematics

The purpose of the course is the study of a topic, which could come from any period (ancient or even newer) and can be selected in consultation with students. An important element of the course is the active participation of students through presentations. Indicative topics can be:

Study of Euclid’s Elements, official foundation of Geometry. The first half of Book I of the Elements, without the fifth postulate and Thales’ contribution. The geometry of the Pythagoreans: Fifth postulate, Pythagorean theorem, quotations from Geometric Algebra, the discovery of incommensurability by Hippasus of Metapontum, infinite anthyphairesis, lateral and diametrical numbers (Books I and II of the Elements). The philosophy of the Pythagoreans and the paradoxes of Zeno. Hippocrates of Chios and meniscus square.

The concepts of infinity and continuum according to Aristotle.

Study of the work of Archimedes.

The discovery of Hyperbolic Geometry, the philosophical-mathematical-physical problem for the concept of “space”, after the foundation of Non-Euclidean Geometry. The official foundation of Geometries by Hilbert in the context of the classical view.

Newton and Leibniz: the founders of Calculus.

• Davis, D. M. (1993). The Nature and Power of Mathematics. Princeton University Press.
• Davis, P. J. & Hersh, R. (1981). The Mathematical Experience. Harvester Press.