On the Infinite: An Interdisciplinary Symposium

Institute Henri Poincaré, October 18 – October 20, 2017 and Sorbonne October 21, 2017

Infinity: the break in the horizon, the “what cannot be counted”, boundless, bottomless, eternal, illimitable and absolute. The infinite encloses physical space; the infinite holds time within itself.

Already in the classical period, philosophers were undone by Zeno’s paradox, that an arrow shot from its bow will never reach its target because it must pass through every point between bow and target, and there are infinitely many such points. For cosmologists, the urgent question is: Is the universe finite or infinite? Will it last forever? And theologians saw in it an attribute of God, and were even prohibited to talk about it.

For the mathematician the infinite is the oil in the machine. For the mathematician who is a set theorist the infinite is a totality—completed, though in Aristotle’s sense, out of view; while at the same time the infinite is essentially open: open “above”, so numberless; but also open inwardly, in the way it copies itself internally over and over again, prints an image of itself into every one of its proper parts, and reprints, and reprints, and reprints, toward an endlessly fractured and ramified whole.

Critical conceptions of the infinite coming from outside of mathematics may coalesce around the concept of *seriality*. In *The Infinite Line* the art historian Briony Fer writes of the various serial strategies available to the artist; how “repetition, splintered into multiple registers, [is] no longer pitched against the aura of a single, unique artwork, so much as against its other selves.”

**In this four-day interdisciplinary symposium we juxtapose lectures by set theorists and other mathematicians with those by art historians, architects, artists and philosophers, in an attempt to create a dialogue across cultures. **

Some of the mathematical talks will be aimed at a general audience.

The symposium is accompanied by an exhibition of the work of the sculptor Fred Sandback.

**Invited Speakers:**

**Yves André** (mathematics, Paris VI)

**Andrew Arana** (philosophy, IHPST Paris)

**Joan Bagaria** (mathematics, Barcelona)

**Emily Brady** (philosophy, Edinburgh)

**Maria Clara Cortés** (art, Universidad Nacional de Colombia)

**Briony Fer** (art history, UCL)

**Sebastian Gandon** (philosophy, Clermont-Ferrand)

**Wilfrid Hodges** (mathematics, QML emeritus)

**Hanna Johansson** (art history, Helsinki)

**Menachem Magidor** (mathematics, Hebrew University)

**Maryanthe Malliaris** (mathematics, University of Chicago)

**Philip Ording** (mathematics, Sarah Lawrence College)

**Juhani Pallasmaa** (architecture, Helsinki)

**Marja Sakari** (art history, Kiasma, Helsinki)

**SMITH** (artist, Paris)

**John Steel** (mathematics, Berkeley)

**Valdimir Tasic** (mathematics, University of New Brunswick)

**Jean-Philippe Uzan** (CNRS, Institut d’Astrophysique de Paris)

**Andres Villaveces** (mathematics, Bogotá)

**Philip Welch** (mathematics, Bristol)

**Hugh Woodin** (mathematics and philosophy, Harvard)

**Exhibition:** *Fred Sandback at the Institute Henri Poincaré.*

**Organizers:**

Michael Harris, Columbia University, New York

Juliette Kennedy, University of Helsinki

Boban Velickovic, Paris Diderot University

**Sponsors:**

Finnish Academy of Science and Letters

Institute Français de Finland

University of Helsinki

Institute Henri Poincaré

European Research Council

Magnus Ehrnrooth Foundation