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existentialtype.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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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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ncatlab.org
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terrytao.wordpress.com
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| | | Many modern mathematical proofs are a combination of conceptual arguments and technical calculations. There is something of a tradeoff between the two: one can add more conceptual arguments to try ... | ||
