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neilmadden.blog | ||
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dvt.name
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| | | | | Gödel's incompleteness theorems have been hailed as "the greatest mathematical discoveries of the 20th century" - indeed, the theorems apply not only to mathematics, but all formal systems and have deep implications for science, logic, computer science, philosophy, and so on. In this post, I'll give a simple but rigorous sketch of Gödel's First Incompleteness ... | |
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cromwell-intl.com
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| | | | | Hypercomputation is a wished-for magic that simply can't exist given the way that logic and mathematics work. Its purported imminence serves as an excuse for AI promoters. | |
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billwadge.com
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| | | | | The famous mathematician Kurt Gödel proved two "incompleteness" theorems. This is their story. By the 1930s logicians, especially Tarski, had figured out the semantics of predicate logic. Tarski described what exactly was an 'interpretation' and what it meant for a formula to be true in an interpretation. Briefly, an interpretation is a nonempty set (the... | |
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cacm.acm.org
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| | | [AI summary] The article discusses the ongoing evolution of the P vs NP problem in computational complexity theory, emphasizing its profound implications for algorithm design, cryptography, and artificial intelligence. It highlights how advances in machine learning and quantum computing are reshaping our understanding of computational limits, while also cautioning against the potential misuse of algorithms in areas like algorithmic bias and surveillance. The piece concludes by reflecting on the philosophical and practical significance of P vs NP, suggesting that its resolution could redefine the boundaries of what is computationally feasible. | ||
