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Full Idea
I'm tempted to say that mathematics is so rich that there are indefinitely many ways to prove anything - verbal/symbolic derivations and pictures are just two.
Gist of Idea
There is no limit to how many ways something can be proved in mathematics
Source
James Robert Brown (Philosophy of Mathematics [1999], Ch. 9)
Book Ref
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.130
A Reaction
Brown has been defending pictures as a form of proof. I wonder how long his list would be, if we challenged him to give more details? Some people have very low standards of proof.
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| 10256 | For intuitionists, proof is inherently informal [Shapiro] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| 10885 | Computer proofs don't provide explanations [Horsten] |