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<strong>Enetz Ezenarro</strong><br> ILCLI & Teachers University School at Vitoria-Gasteiz ILCLI Open Seminar. December 10, at 12:30. Room A4<br> <h2>What do we owe to Bourbaki?</h2> <h3>Abstract</h3><p>In the field of the 'internal foundations of mathematics', Structuralism is mainly the conception of mathematics presented by Bourbaki in his 'Éléments de Mathématique' [Mashaal (2006), Bourbaki. A secret society of mathematicians]. Following the major re-organisation of pure mathematics carried out in that work, taking as its core concept that of mathematical structure, he came to define mathematics as a science of structures. From today's perspective some decades after the last contribution by Bourbaki, structures, understood in the broadest sense, do not seem to be the central organising principle of mathematics, as aimed by Bourbaki [Borel (1998), Twenty-five years with Nicolas Bourbaki, 1949-1973; www.ams.org/notices/199803/borel.pdf]. Nevertheless, it is true that they remain one of the basic pillars for a coherent organisation of the field. The purpose of the talk is to present Bourbaki's main contributions and to assess their relevance for our current view on mathematics.</p>