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math.HO2022
The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics
Stephen Wolfram
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computatio…
math.HO2021★ 2 cited
Where Did Combinators Come From? Hunting the Story of Moses Schönfinkel
Stephen Wolfram
Combinators were a key idea in the development of mathematical logic and the emergence of the concept of universal computation. They were introduced on December 7, 1920, by Moses S…
math.HO2021
The Empirical Metamathematics of Euclid and Beyond
Stephen Wolfram
As an example of empirical metamathematics, we present a detailed study of the dependency structure of the 465 theorems in Euclid's Elements, finding empirical signatures of concep…