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liorpachter.wordpress.com | ||
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rjlipton.com
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| | | | | A new way to write mathematics Vladimir Voevodsky won the Fields Medal in 2002 for his work on homotopy theory of algebraic varieties. Using his pioneering methods he proved, among many other things, a deep conjecture of John Milnor, that had been open for decades. Today I want to talk about, no, rant about, a... | |
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scottaaronson.blog
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| | | | | Over at Theoretical Computer Science StackExchange, an entertaining debate has erupted about the meaning and validity of the Church-Turing Thesis. The prompt for this debate was a question asking for opinions about Peter Wegner and Dina Goldin's repetitive diatribes claiming to refute "the myth of the Church-Turing Thesis"---on the grounds that, you see, Turing machines... | |
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math.andrej.com
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| | | | | [AI summary] The discussion revolves around the philosophical and methodological pluralism in mathematics, emphasizing that mathematics is a human-made construct with historical developments rather than an absolute, universal truth. Key points include the idea that different mathematical frameworks (e.g., classical vs. intuitionistic logic, paraconsistent logic) represent distinct 'worlds' of mathematics, each with its own standards and validity. The conversation highlights the importance of acknowledging these pluralistic perspectives without assuming a single, unifying foundation. It also touches on the role of context, the evolution of mathematical concepts, and the implications of relativism for the future of mathematics. The discussion underscores that ... | |
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mycqstate.wordpress.com
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| | | This post is a follow-up on some somewhat off-hand comments that I made earlier regarding the notion of truth in a "proof-based" discipline such as pure mathematics or theoretical computer science. Since the former is easier to circumscribe and also has a larger literature available on it, for the purposes of the post I will... | ||
