Joint Colloquium: Henrik Kragh Soerensen -- The Irony of Romantic Mathematics: NOTE UNUSUAL TIME AND VENUE

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 “solvability” rather
than “solution”.  Thereby, they shifted their focus to investigating the
representability within certain (restricted) formal systems, yielding unforeseen
results.