A Model-Based Approach for The Demonstration of Fermat’s Last Theorem

Xu, Hong

doi:10.11648/j.pamj.20170605.12

Cited by 1 publication

(1 citation statement)

References 18 publications

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“…It is probably much more difficult (100 pages using mathematics developed long after Fermat) and stood unsolved for twice as long. However, as in the present case, additional time, confidence and new conceptualizations have produced multiple remarkably shorter proofs, and new implications for other fields such as biology [8].…”

Section: Discussionmentioning

confidence: 58%

Entropy-Like State Counting Leads to Human Readable Four Color Map Theorem Proof

Shuler¹

2018

PAMJ

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The problem of how many colors are required for a planar map has been used as a focal point for discussions of the limits of human direct understanding vs. automated methods. It is important to continue to investigate until it is convincingly proved map coloration is an exemplary irreducible problem or until it is reduced. Meanwhile a new way of thinking about surfaces which hide N-dimensional volumes has arisen in physics employing entropy and the holographic principle. In this paper we define coloration entropy or flexibility as a count of the possible distinct colorations of a map (planar graph), and show how a guaranteed minimum coloration flexibility changes based on additions at a boundary of the map. The map is 4-colorable as long as the flexibility is positive, even though the proof method does not construct a coloration. This demonstration is successful, resulting in a compact and easily comprehended proof of the four color theorem. The use of an entropy-like method suggests comparisons and applications to issues in physics such as black holes. Therefore in conclusion some comments are offered on the relation to physics and the relation of plane-section color-ability to higher dimensional spaces. Future directions of research are suggested which may connect the concepts to not only time and distance and thus entropic gravity but also momentum.

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Section: Discussionmentioning

confidence: 58%

Entropy-Like State Counting Leads to Human Readable Four Color Map Theorem Proof

Shuler¹

2018

PAMJ

View full text Add to dashboard Cite

show abstract

A Model-Based Approach for The Demonstration of Fermat’s Last Theorem

Cited by 1 publication

References 18 publications

Entropy-Like State Counting Leads to Human Readable Four Color Map Theorem Proof

Entropy-Like State Counting Leads to Human Readable Four Color Map Theorem Proof

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