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2 ideas

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

13007

Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order

13701

A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider]