In book VII of the Elements, Euclid develops some fundamental results from number theory. How much of this, if any, can be reproduced in Hilbert's axiomatization? It seems to me that the answer is close to nothing, since Hilbert's formalization can't even state the basic arithmetical concepts. Is this correct? On what basis do we today differentiate arithmetic from geometry, that Euclid did not have (or respect)?
2026-02-23 13:46:23.1771854383
How much of Euclid's number theory can be reproduced in Hilbert's axiomatization of geometry?
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