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cornellmath.wordpress.com | ||
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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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xorshammer.com
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| | | | | Here's a puzzle: You and Bob are going to play a game which has the following steps. Bob thinks of some function $latex f\colon \mathbb{R}\to\mathbb{R}$ (it's arbitrary: it doesn't have to be continuous or anything). You pick an $latex x \in \mathbb{R}$. Bob reveals to you the table of values $latex \{(x_0, f(x_0))\mid x_0\ne x\}$... | |
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scottaaronson.blog
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| | | | | In Michael Sipser's Introduction to the Theory of Computation textbook, he has one Platonically perfect homework exercise, so perfect that I can reconstruct it from memory despite not having opened the book for over a decade. It goes like this: Let f:{0,1}*?{0,1} be the constant 1 function if God exists, or the constant 0 function... | |
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caitlinsanswersforhumanitiesclass.wordpress.com
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| | | This is the excerpt for your very first post. | ||
