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scottaaronson.blog | ||
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cornellmath.wordpress.com
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| | | | | When discussing the validity of the Axiom of Choice, the most common argument for not taking it as gospel is the Banach-Tarski paradox. Yet, this never particularly bothered me. The argument against the Axiom of Choice which really hit a chord I first heard at the Olivetti Club, our graduate colloquium. It's an extension... | |
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reportofanimals.com
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| | | | | DISCLAIMER: This is an essay I wrote for my Masters degree in 2023, part of a series I will be putting on this site to get me started. While I have changed some of my views and found new lines of inquiry since I wrote this, I feel there is value in it and after... | |
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rjlipton.com
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| | | | | Another proof idea using finite automata Steve Cook proved three landmark theorems with 1971 dates. The first has been called a "surprising theorem": that any deterministic pushdown automaton with two-way input tape can be simulated in linear time by a random-access machine. This implies that string matching can be done in linear time, which inspired... | |
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xorshammer.com
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| | | In the book A=B, the authors point out that while the identity $latex \displaystyle{\sin^2(|10 + \pi x|) + \cos^2(|10 + \pi x|) = 1}$ is provable (by a very simple proof!), it's not possible to prove the truth or falsity of all such identities. This is because Daniel Richardson proved the following: Let $latex \mathcal{R}$... | ||
