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Conceptions of Geometry from Klein through Hilbert to Weyl (Sponsored by the International Philosophy of Mathematics Association)

Thursday, 3 November 2016

09:00 - 10:30

Piedmont 1 (12th Floor)

**Chair:** Colin McLarty, Case Western Reserve University

Felix Klein’s famous Erlangen Program laid out a broadly influential idea of organizing mathematics around geometry and geometry around group theory, though the Program has always been more cited than read, and Klein’s influence was actually not so focused as that paper. One of his most influential moves was to promote the career of David Hilbert. The two of them built the great Mathematics Department of early 20th century Gottingen. Hermann Weyl, who eventually led that Department, took their influence much farther into physics. The three speakers will describe various related but distinct aspects of their geometric projects including transformation groups in geometry and physics, and the relation of axiomatic geometry to applications.

The ideas are important in current philosophy of mathematics for their reflection on modern algebraic and geometric methods of treating structure, and for the relation of pure to applied mathematics, and for understanding Hilbert’s conception of axiomatic foundations. And especially through Weyl the relate to early and current issues of understanding symmetry in modern physics.

*Weyl, Identity, Indiscernibility*- Otavio Bueno, University of Miami,

*Hilbert’s Geometry and Mathematical Truth*- Eileen Nutting, University of Kansas,

*Klein’s Erlangen Program and Physical Geometry in the Early Twentieth Century*- Sahotra Sarkar, University of Texas at Austin,