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Arithmetic, geometry, and music in Giovanni Pisano’s pulpit (1301-1310), Duomo di Pisa

Pisa is the international symbol of improbable constructions and therefore a fitting location for this week’s workshop.  Pisa is also a fitting location for meditating on the eternal and impossible question:  do we engage in mathematics because we find it beautiful, or do we find mathematics beautiful because of our programming?  Are Pisa’s medieval arcades beautiful because we are used to them or do we admire Pisa for the beauty of its medieval architecture?

In addition to the Roman sarcophagi that littered Pisa’s underworld and were recycled in medieval times to house the remains of political and military citizens “di primario spicco,” Pisa’s Camposanto contains the gigantic (5.6 x 15 m) 14th century fresco Il trionfo della morte which might have served as a reminder of the urgency of completing the program of this week’s workshop, but which is undergoing restoration and is therefore not visible to the public.  It seems to me the workshop provides a striking illustration of the complex interplay between freedom and inevitability in the design of a mathematical theory, in this case the mod p Langlands program, whose ultimate goals are being defined, democratically as far as I can tell, through workshops and conferences like this one.

Pisa’s medieval walls are also decorated with a variety of political statements.  Someone found it worth his or her while to design a stencil to celebrate an American mathematical personality:

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Seen on a wall in central Pisa. The caption reads “strike where it hurts the most.”