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| | windowsontheory.org
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| | (see also pdf version) Quantum computing is one of the most exciting developments of computer science in the last decades. But this concept is not without its critics, often known as "quantum computing skeptics" or "skeptics" for short. The debate on quantum computing can sometimes confuse the physical and mathematical aspects of this question,...
| | scottaaronson.blog
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| | Over at Theoretical Computer Science StackExchange, an entertaining debate has erupted about the meaning and validity of the Church-Turing Thesis. The prompt for this debate was a question asking for opinions about Peter Wegner and Dina Goldin's repetitive diatribes claiming to refute "the myth of the Church-Turing Thesis"---on the grounds that, you see, Turing machines...
| | 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 ...
| | mathbabe.org
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| Brian Conrad is a math professor at Stanford and was one of the participants at the Oxford workshop on Mochizuki's work on the ABC Conjecture. He is an expert in arithmetic geometry, a subfield of number theory which provides geometric formulations of the ABC Conjecture (the viewpoint studied in Mochizuki's work). Since he was asked...