The four colour theorem and computer proof: a maths EPQ idea
A title to start from
Why was the computer-assisted proof of the four colour theorem controversial, and should it be trusted?
Why it works as an EPQ
You can prove the five colour theorem yourself and then weigh the arguments about a proof no person can check by hand.
Scope and difficulty
Solid. Solid. The five colour proof plus a careful discussion is plenty; do not attempt the four colour proof.
The maths
Builds on these A Level topics: Proof.
You would learn:
- Graphs and planar graphs
- Euler's formula V − E + F = 2
- Proof by induction on vertices
One possible plan
- Turn map colouring into graph colouring.
- Prove Euler's formula and deduce every planar graph has a vertex of degree at most 5.
- Prove the five colour theorem.
- Evaluate the 1976 computer proof and later formal verification.
Pitfalls
- Confusing maps with graphs part way through.
- Turning the evaluation into opinion with no criteria.
Where to start reading
- Four Colors Suffice (Robin Wilson)
- Search for: five colour theorem proof Kempe chains
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All pure maths ideas · all 93 ideas
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