Flyspeck I: Tame Graphs

Nipkow, Tobias; Bauer, Gertrud; Schultz, Paula

doi:10.1007/11814771_4

Cited by 36 publications

(39 citation statements)

References 7 publications

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“…(The definition of tameness is rather intricate; its key property is that the set of tame graphs includes all graphs that give a potential counterexample to the conjecture.) G. Bauer's thesis, together with subsequent work with T. Nipkow, completes the formal proof of the enumeration of tame graphs [38]. Section 6 gives a summary of this formalization project.…”

Section: Formal Proof Of the Kepler Conjecturementioning

confidence: 96%

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A Revision of the Proof of the Kepler Conjecture

Hales

Harrison

McLaughlin

et al. 2009

Discrete Comput Geom

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The Kepler conjecture asserts that no packing of congruent balls in threedimensional Euclidean space has density greater than that of the face-centered cubic packing. The original proof, announced in 1998 and published in 2006, is long and complex. The process of revision and review did not end with the publication of the proof. This article summarizes the current status of a long-term initiative to reorganize the original proof into a more transparent form and to provide a greater level of certification of the correctness of the computer code and other details of the proof. A final part of this article lists errata in the original proof of the Kepler conjecture.

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Section: Formal Proof Of the Kepler Conjecturementioning

confidence: 96%

“…Now we give a top-level overview of the formalization and proof of completeness of the enumeration of tame graphs in HOL. For details, see [38]. The complete machine-checked proof, over 17000 lines, is available online in the Archive of Formal Proofs at afp.sf.net [2].…”

Section: Theorem 1 Any Tame Plane Graph Is Isomorphic To a Graph In Tmentioning

confidence: 99%

A Revision of the Proof of the Kepler Conjecture

Hales

Harrison

McLaughlin

et al. 2009

Discrete Comput Geom

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“…Flyspeck was ultimately successful, confirming and simplifying Hales's argument [57]. Some of the formal proofs were done using Isabelle [58].…”

Section: Formalizing Mathematicsmentioning

confidence: 78%

Computational logic: its origins and applications

Paulson¹

2018

Proc. R. Soc. A.

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Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the ‘logic for computable functions (LCF) approach’ pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users’ code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation. The main application of these techniques has been to prove the correctness of hardware and software systems, but increasingly researchers have been applying them to mathematics itself.

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“…There are a few general formalizations of graph theory available in various theorem provers, for example [9,10,20]; but often proof developments rather use specialized formalizations of certain aspects of graph theory [16,24] to ease the proof. For the Girth-Chromatic Number theorem, the common definition of graphs as pairs of vertexes and edges seems quite optimal.…”

Section: Related Workmentioning

confidence: 99%