Dense Sphere Packings: A Blueprint for Formal Proofs (London Mathematical Society Lecture Note Series, Series Number 400) 1st Edition by Thomas Hales (PDF)

Description

The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it accessible for the first time to a broad mathematical audience. The book also presents solutions to other previously unresolved conjectures in discrete geometry, including the strong dodecahedral conjecture on the smallest surface area of a Voronoi cell in a sphere packing. This book is also currently being used as a blueprint for a large-scale formal proof project, which aims to check every logical inference of the proof of the Kepler conjecture by computer. This is an indispensable resource for those who want to be brought up to date with research on the Kepler conjecture.

User’s Reviews

Editorial Reviews: Review “… interesting and unusual book … beautifully written and is full of interesting historical notes. Moreover, each chapter is equipped with a very helpful summary, and many technical arguments are accompanied by a conceptual informal discussion. The book also features a detailed index and a nice bibliography. It is bound to become an indispensable resource for anyone wishing to study Kepler’s conjecture.” Zentralblatt MATH Book Description The definitive account of the recent computer solution of the oldest problem in discrete geometry. About the Author Professor Thomas Hales is Andrew Mellon Professor at the University of Pittsburgh. He is best known for his solution to the 400-year-old Kepler conjecture and is also known for the proof of the honeycomb conjecture. He is currently helping to develop technology that would allow computers to do mathematical proofs. His honors include the Chauvenet Prize of the MAA, the R. E. Moore Prize, the Lester R. Ford Award of the MAA, the Robbins Prize of the AMS and the Fulkerson Prize of the Mathematical Programming Society. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Kepler conjectured that no packing of non-overlapping, equal-sized spheres in 3-space achieved a density greater than the density of the “cannonball packing”. Hales managed to prove this conjecture, but the proof is long, sometimes subtle, and relies on extensive computer calculations. The referees of his paper were unwilling to give the paper their unreserved seal of approval, so Hales set out to redo his proof, this time in a computer-verifiable manner. This is the most rigorous standard of proof available to mathematicians today.This volume is a roadmap: it outlines the computer-verifiable proof that is currently under construction. But this book is not intended for computers: it gives the human reader a good and illustrative overview of the mathematics that goes into the proof. As such, it is a no-brainer buy for any mathematician with an interest in the topic!

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