Type: Seminar

Modified: Tue 14 Oct 2008 1515; Thu 16 Oct 2008 1321

Distribution: World

Expiry: 17 Oct 2008

CalTitle1: Joint Colloquium: Henrik Kragh -- The Irony of Romantic Mathematics: NOTE UNUSUAL TIME

Auth: carberry@cpe-124-176-105-150.nsw.bigpond.net.au

Speaker: Assoc. Prof. Henrik Kragh Soerensen (University of Aarhus) Title: The Irony of Romantic Mathematics Date: Friday, 17 October 2008 Time: 1:00 pm (NOTE TIME CHANGE) Venue: Room 173 Carslaw Building, University of Sydney (NOTE ROOM CHANGE) We will meet at 11:30 AM at the outside foyer on the second floor to take the Speaker to lunch at the Forum restaurant in the Darlington Centre . Please let me know if you plan to join us. Abstract: During the first part of the nineteenth century, mathematics underwent a number of important cognitive and institutional transformations. In this talk, I wish to illustrate and contextualise some of these transformations by contextualising a number of examples from the mathematical production of mathematicians such as N. H. Abel, C. F. Gauss, and N. Lobachevsky within the romantic period. Many of the most famous and productive mathematicians of early nineteenth century were prototypical romantic heroes --- neglected geniuses who died young, suffering the material world while studying the immaterial mathematical entities. However, the romantic influence over mathematics during that period extended well beyond the purely biographical. Especially in the Germanic romantic era, mathematics was immersed in a cultural embedding that will allow us to discuss perspectives on romantic irony from a mathematical viewpoint. In the first part of the nineteenth century, mathematics developed in an increasingly conceptual direction. As part of this transition, mathematicians began asking fundamentally new kinds of questions that led to new types of answers. Instead of asking for explicit formulae as results, mathematicians began to question the very possibility of such formulae. At the same time, other discoveries (such as non-Euclidean geometry) led mathematicians to distance their pursuit from the investigation of nature, turning it into an autonomous discipline concerned with an immaterial mathematical realm. Since the fifteenth century, mathematicians had searched for a general formula for solving equations of all degrees. However, around 1830 and coinciding with the late romantic period, the new concept-centred approach led innovative young mathematicians such as Abel and Galois to reformulate the question in terms of â€œsolvabilityâ€ rather than â€œsolutionâ€. Thereby, they shifted their focus to investigating the representability within certain (restricted) formal systems, yielding unforeseen results.