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intellectualmathematics.com | ||
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njwildberger.com
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| | | | | Modern mathematics is enormously complicated and sophisticated. It takes some courage, and perhaps some foolishness, to dare to suggest that behind the fancy theories lie serious logical gaps, and indeed error. But this is the unfortunate reality. Around the corner, however, is a new and more beautiful mathematics, a more honest mathematics, in which everything... | |
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www.quantamagazine.org
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| | | | | Number theorist Andrew Granville on what mathematics really is - and why objectivity is never quite within reach. | |
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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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| | | Today I'd like to sketch a question that's been pushing me in a lot of different directions over the past few years --- some sane, others less so; few fruitful, but all instructive. The question is motivated by the problem of placing upper bounds on the amount of entanglement needed to play a two-player non-local... | ||
