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Toposes and their place in mathematics: an interview with Olivia Caramello

Olivia Caramello and Nathan Carruth

Prof. Olivia Caramello, President of the Grothendieck Institute and Coordinator of its Centre for Topos Theory and its Applications (CTTA), gave an interview for the Notices of the International Consortium of Chinese Mathematicians (ICCM), conducted by Nathan Thomas Carruth of Tsinghua University (Beijing).

In the interview, given on the occasion of the first edition of the International Congress of Basic Science, she extensively talks about her theory of toposes as “bridges”, which provides a set of techniques allowing to effectively use toposes as unifying spaces in mathematics and is currently developed by the CTTA.

She also gives her perspective on the role that toposes can play in connection with the emergence of new forms of artificial intelligence based on structures and invariants, and elaborates on the importance of logic and category theory for developing mathematics in a dynamical and interdisciplinary way. In the final part of the conversation, Prof. Caramello also talks about her approach to mathematical work and offers advice to young researchers based on her own experiences and Grothendieck’s ideas about creativity.

The full text of the interview, which will be published in the ICCM Notices, is available at the following link.

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