Titlebook: Contemporary Mathematical Thinking; Frédéric Patras Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive license to

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The Origins of Modern Mathematics,The creation of modern mathematics standards for definitions and proofs, as well as for the organisation of the corpus, took a long time. The analysis of preliminary stages leads to highlight the gradual emergence of a new understanding of mathematics in the work of Gauss, Galois, Dedekind and Frege, among others.

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Contemporary Mathematical Thinking978-3-031-27548-7Series ISSN 0166-6991 Series E-ISSN 2542-8292

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https://doi.org/10.1057/9781137339614cturalism endeavour, are central to 20th century mathematics. However, the very idea of structure is less precise than it would seem at first sight and unfolds in various ways. One is oriented towards axiomatics. Another, more programmatic, refers instead to a general regulating concept of thought.

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https://doi.org/10.1057/9781137339614ts in contemporary mathematics, which would require new ideas and new ambitions. This chapter looks further into Bourbaki’s mathematical epistemology and investigates its connexions with category theory.

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