Prologue -- Dreams / Michael Atiyah -- Interval -- Pitiless reality / Alain Connes -- From Tasmania with love / Dirk Kreimer -- Puzzles / Karen Yeats -- Structured fury / Paulo Almeida -- A tartar desert / Ngô Bao Châu -- Exoticism / Paul-Olivier Dehaye -- Entr'acte -- Curiosity / Sophie de Buyl -- The paving stones of the Route de Charres / Thibault Damour -- Pause -- From 1948 to the present day / Cécile DeWitt -- Knowing, understanding, discovering / Yvonne Choquet-Bruhat -- Farewell to Alexander's sword / Arndt Benecke -- Interlude -- Dialogue on the scales of life / Annick Lesne -- Teatime -- Lost in translation / Nikita Nekrasov -- Thought technology : the pursuit of structure / Yiannis Vlassopoulos -- Mathematical physics / Ivan Todorov -- In praise of tautology / Anna Wienhard -- New worlds / Giovanni Landi -- The music pavilion / Pierre Deligne -- Long live the whale / Claire Voisin -- What does one write on it? / Jean-Marc Deshouillers -- Solidarity / Pierre Cartier -- North-South / Ali Chamseddine -- Privilege / Christophe Breuil -- What do mathematicians do? / Laurent Berger -- Fractalitas / Matilde Lalin -- Mathematics, biology and neurobiology / Jürgen Jost -- Mathematics in the biological sciences / Henry Tuckwell -- Intermezzo -- The unravelers / Katia Consani -- Long live the machine / Oscar Lanford -- Arriving in paradise / Jürg Fröhlich -- Go to the board! / Sylvie Paycha -- Lunch at IHES (1975-1995) / Dennis Sullivan -- Happy day at Bures-sur-Yvette in the sixties / Jacques Tits -- The flowers of Maths / Wendy Lowen -- The arcane in the mundane / Michael Berry -- Allegory / Nathalie Deruelle -- Coffee break -- Correspondence / Minoru Wakimoto -- Ilan / Victor Kac -- The four mysteries of the world / Mikhaïl Gromov -- Flashes / Étienne Ghys -- State of grace / David Eisenbud -- Violins / Christophe Soulé -- Mathematics as culture and knowledge / Matilde Marcolli -- A question of time / Alessandra Carbone -- "The times, they are a-changing" / Jean-François Méla -- The vision / Jean-Pierre Bourguignon -- Taming mathematics / Denis Auroux -- Three lights / Alexandr Usnich -- Beyond numbers / Maxim Kontsevitch.