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Single Idea 17942

[filed under theme 14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof ]

Full Idea

The proof of the four-colour theorem raises questions about whether a 'proof' that no one understands is a proof.

Gist of Idea

Can a proof that no one understands (of the four-colour theorem) really be a proof?

Source

Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.6)

Book Ref

Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.153

A Reaction

The point is that the theorem (that you can colour countries on a map with just four colours) was proved with the help of a computer.

The 5 ideas with the same theme [proofs which also reveal why something is true]:

13231 Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
17933 Reductio proofs do not seem to be very explanatory [Colyvan]
17935 If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
17934 Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
17942 Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]