Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas cover image

AMA | December 2023

Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas

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Challenges of Formalizing Mathematical Proofs

The standards for rigor in math papers are higher than in physics papers, but they still fall short of the level of formalization established by Russell and Whitehead in their attempt to establish the foundations of arithmetic. The process of making progress in math involves examining assumptions, conclusions, and careful derivations. The defining feature of capitalism could be argued to be the private ownership of capital, rather than the free market.

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