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6. Mathematics / A. Nature of Mathematics / 6. Proof in Mathematics

[establishing new certainties from a starting point]

7 ideas
To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell]
For intuitionists, proof is inherently informal [Shapiro]
There is no limit to how many ways something can be proved in mathematics [Brown,JR]
Computers played an essential role in proving the four-colour theorem of maps [Brown,JR]
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
Computer proofs don't provide explanations [Horsten]