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Formalize!(?) – 4 — A philosophical & educational perspective on formalization in mathematics
15 Jan 2024 • online, Any Location (virtual event)
This series of events began with the theme of foundations in the context of automated theorem proving: What are the chances and problems of the act of formalization in the context of mathematics? It is often said, that all of mathematics can be reduced to first-order logic and set theory. The derivation indicator view says that all proofs stand in some relation to a derivation, i.e. a mechanically checkable syntactical objects following fixed rules, that would not have any gaps. For a long time this was a mere hope. There may have been proofs of concepts from early logicists but derivation never played a big role in mathematical practice. The modern computer might change this. Interactive and automated theorem provers promise to make the construction of a justification without any gaps feasible for complex mathematics. Is this promise justified? Will the future of mathematical practice shift to more formal mathematics? Should it? We hope to illuminate such questions and focus especially on what these developments mean for the future of the curriculum of university students. After three years on the topic, we have realized that this context is too narrow to understand formalization and thus we have we added a yearly theme (although not all talks are necessarily aligned with it). This year we focus on historical perspectives: How were different formal systems implemented? How much choice was there? Is our current view an ironed out history, written by the winner of the debate?
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