Si vous me permettez de citer l'abstract de Georges Gonthier à propos de la démonstration du théorème des 4 couleurs, vous pourrez constater que l'exercice ne se limite pas du tout à un « bête comptage de cas sans intérêt » et qu'il a également été l'occasion de comprendre et d'apporter de nouvelles idées.
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Our effort turned out to be more than just an exercise in verification; having to definine rigorously all key concepts provided new mathematical insight into the concept of planarity. Planarity has topological and combinatorial characterizations, which are often confused in arguments that are both pictorially appealing and logically incomplete. The rigor of our computer proof imposed a strict separation between the two.
We developed a purely combinatorial theory of planarity based on a symmetrical presentation of hypermaps, which greatly simplified the proof. The theory supplies an elegant analogue of the Jordan Curve property, which allowed us to prove the Theorem under minimal topological
assumptions, without appealing to Jordan Curve theorem.
[^] # Re: En souvenir de son infirmation de la conjecture des quatre couleurs.
Posté par Igor_d . En réponse au journal Martin Gardner (1914-2010). Évalué à 3.
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Our effort turned out to be more than just an exercise in verification; having to definine rigorously all key concepts provided new mathematical insight into the concept of planarity. Planarity has topological and combinatorial characterizations, which are often confused in arguments that are both pictorially appealing and logically incomplete. The rigor of our computer proof imposed a strict separation between the two.
We developed a purely combinatorial theory of planarity based on a symmetrical presentation of hypermaps, which greatly simplified the proof. The theory supplies an elegant analogue of the Jordan Curve property, which allowed us to prove the Theorem under minimal topological
assumptions, without appealing to Jordan Curve theorem.
source : http://www.springerlink.com/content/3243j73u8078486t/