Unverified50% confidenceOpinionExact time
Thurston's core argument is that progress in mathematics cannot be measured solely by "whether a theorem has been proved"; real progress lies in changes in how humans understand.
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10/14/2026
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UnverifiedThurston distinguished between "formal proof" and "mathematical understanding": the former is a chain of logic written on paper, while the latter is a knowledge structure in the mathematician's mind that is transferable, explainable, and open to further development.72% similarUnverifiedDavid Deutsch argues in his book The Beginning of Infinity that the key to scientific progress lies in generating hard-to-vary explanations.66% similarUnverifiedSome mathematicians believe that proofs which cannot be verified step by step by the human brain do not carry sufficient mathematical meaning.63% similarUnverified工程上的进展与科学上的突破是两个不同概念，前者是对已有范式的量化改善，后者意味着新知识的创造62% similarUnverifiedDeMillo 等人认为数学定理被信任是因为经历了社会过程（被数学家反复阅读、检验、引用），而程序的形式化证明缺少这种社会过程61% similar
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