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juliawolffenotes.home.blog | ||
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gowers.wordpress.com
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| | | | | This post is intended to accomplish several things at once. First and foremost, I want to explain (not just in the post) why I have been interested in Borel determinacy and in the natural proofs barrier. Roughly speaking (or should I say tl;dr?) I think that Martin's proof of Borel determinacy has features that might... | |
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mnielsen.github.io
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| | | | | [AI summary] The text explores the challenges of understanding abstract mathematical concepts and the role of representation in problem-solving. It emphasizes the importance of converting unfamiliar ideas into terms of known concepts, using examples like high-dimensional spaces and the irrationality of √2. The author argues that 'genius' is often the result of systematic practice with multiple representations rather than innate talent. The text concludes by suggesting the need for systems that support this process of representation mastery, such as interactive environments or tools that aid in cognitive elaboration. | |
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jiggerwit.wordpress.com
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| | | | | What follows are the opening paragraphs of a pdf document giving an argument for controlled natural languages in mathematics. At the recent Big Proof 2 conference in Edinburgh, I realized that a case must be made for developing a controlled natural language for mathematics. There is little consensus on this issue, and mathematicians and computer... | |
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daniellefong.com
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| | | The following occurred to me on a run about two years ago: It's not given much press, but the the Halting Problem is intimately related to Gödel's First Incompleteness Theorem. Indeed it produces it as a correllary. Historically, Gödel's incompleteness results were proved by hacking arithmetic into a Turing complete system, and this is still... | ||
