Simplicity via Complexity: Sandboxes, Reading Novalis

  • Andrés VillavecesEmail author
Part of the Mathematics, Culture, and the Arts book series (MACUAR)


When the invitation to a meeting on simplicity arrived, I initially had a sense that the “simplicity question” seemed unidirectional and perhaps all too well posed. It seemed initially to play too well with my own experience. (As a mathematician, one of my most sustained, energy-draining, and time-consuming struggles often seems to be with various forms of simplification.) The philosophical issue seemed almost flat. Yet lurking beneath the surface of this seemingly relentless simplification there is an opposite movement, a dual force. Looking more carefully underneath that unidirectional move toward simplification, I started finding strong elements of a move in the opposite direction, perhaps aptly called “complexification.” This paper centers on the spiraling, back-and-forth movement between simplification and complexification, and on the central role of complexification as part of the simplification process.



I wish to thank the organizers of the meeting “Simplicity: Ideals of Practice in Mathematics & the Arts” (Juliette Kennedy, Roman Kossak, and Philip Ording) for the invitation to a wonderful event. I also thank the referee for a very insightful reading that resulted in sharper formulations and the proofreader for very useful suggestions. I am also in debt to Jan Zwicky for her extremely insightful comments on an earlier version of this essay, on both the content and the writing. In many ways her amazing way of reading made me see with a different contrast some of my own assertions. Finally, I also want to mention many fruitful conversations with John Baldwin, Alex Cruz, Juliette Kennedy, Alejandro Martín, Jouko Väänänen, and Fernando Zalamea on subjects ultimately connected with these musings.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversidad Nacional de ColombiaBogotáColombia

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