Publication: Local-Global in Mathematics and Painting
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2005
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MIT Press
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Abstract
Twentieth century mathematicians have succesfully mastered a method or way of looking that combines local and global tools, and which has lead, for example, to the resolution
of long standing open problems such as Fermat´s Last Theorem2 and the Conjecture of Taniyama, Shimura and Weil. In parts 1 and 2 we will give a brief description of this way of looking, which we will then use, in part 3 as well as in the appendix, to analyse three concrete paintings of Pablo Picasso.
When Michele Emmer invited me to participate in the second volume of “The Visual Mind”, I was already deeply inmersed in an on-going process that has been moving quite
different people -most of us mathematicians, painters, musicians and architects-, for a long time. This process has lead us to analyze, in conversations and reflections as well as in concrete pieces of work, what we have been calling “transmission of knowledge”, in its many facets,
starting from its personal, intellectual and professional impact on us and our work.
As part of this process, in the spring of 1997 Laura Tedeschini-Lalli invited me to participate with a short cycle of conferences in the mathematics course she was then teaching at the School of Architecture, University Roma 3. During the mini-course, whose material can be found in [4] and [5], I reflected on the evolution of the concept of space in mathematics and painting during the XIXth. and XXth. centuries. When trying to understand the mathematical
notions and tools developed along these centuries, I invited the students to, and provided the material for,keep in mind the art painted at each specific time as a raphical reference from where to select some of the characteristics of the abstraction process we were looking at in mathematics.
While preparing the project required for the course, some of the students asked Tedeschini-Lalli if it would be possible to work in the opposite, complementary, direction: to keep in mind the (abstract) tools being used by the mathematical community at a specific time while looking at artworks, in order to select some questions, and a method. This question lead Tedeschini-Lalli and her students to the analysis of Maya with Doll (see appendix). Although
the possibility of working in the direction they follow had already emerged in many of the conversations with mathematicians and artists that have nurtured and given shape to this process along the years, the study of Maya with Doll was the first actual contribution in this
direction, and the one that gave me the push to trust my pencil as a tool of deep thought outside mathematics.
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Appendix by Laura Tedeschini-Lalli
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Citation
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