How geometry became structural

Beschreibung

Abstract: Structuralism in the philosophy of mathematics is, roughly put, the view
that mathematical theories study abstract structures or the structural
properties of their subject fields. The position is strongly rooted in modern
mathematical practice. In fact, one can understand structuralism as an
attempt to come to terms philosophically with a number of wide-ranging
methodological transformations in 19th and early 20th century
mathematics, related to the rise of modern geometry, number theory, and
abstract algebra. The present talk will focus on the geometrical roots of
structuralism. Specifically, we will survey some of the key conceptual
changes in geometry between 1860 and 1910 that eventually led to a
“structural turn” in the field. This includes (i) the gradual implementation
of model-theoretic techniques in geometrical reasoning, for instance, the
focus on duality and transfer principles in projective geometry; (ii) the
unification of geometrical theories by algebraic methods, specifically, by
the use of transformation groups in Felix Klein’s Erlangen Program; and
(iii) the successive consolidation of formal axiomatics in work by Hilbert
and others.

Zeitraum	27 Nov. 2019
Ereignistitel	Mathematical Colloquium
Veranstaltungstyp	Vortragsreihe, Kolloquium
Ort	Wien, ÖsterreichAuf Karte anzeigen
Bekanntheitsgrad	International