A Proof of Kepler Conjecture in Annals of Mathematics 162 No. 3 pp. 1065-1185, November 2005 [FIRST PROOF OF THE KEPLER CONJECTURE]

Princeton University Press, 2005. 1st Edition. FIRST EDITION IN ORIGINAL WRAPPERS OF THE FIRST PROOF OF THE KEPLER CONJECTURE. Complete issue.

In 1611, Johannes Kepler speculated that a pyramid was the most efficient arrangement of spherical objects. The Kepler or honeycomb conjecture "is a mathematical theorem that states that no arrangement of equally sized spheres has a greater average density than that of face-centered cubic packing." But Kepler couldn't prove it - nor could a myriad of mathematicians since.

Though it had been determined that there are infinite ways to stack infinitely many spheres, most were variations on only a few thousand themes. Following an idea by the Hungarian mathematician Laszlo Fejes Toth, in the late 1990s, American mathematician Thomas Callister Hales "broke the problem down into the thousands of possible sphere arrangements that mathematically represent the infinite possibilities, [then he] used software to check them all" (Aron, Proof Confirmed, New Scientist, 12 August 2014).

In 1998, Hales and his graduate student Samuel Ferguson first presented progress what they called ‘The Flyspeck Project'. Essentially, they announced that they had completed the proof, but were unable to publish it because at "that stage, it consisted of 250 pages of notes and 3 gigabytes of computer programs, data and results.

"Despite the unusual nature of the proof, the editors of the Annals of Mathematics provided it was accepted by a panel of twelve referees. In 2003, after four years of work, the head of the referee's panel... reported that the panel were "99% certain" of the correctness of the proof, but they could not certify the correctness of all of the computer calculations" (Wikipedia).

By 2005, the Annals finally felt able to publish Hales work - the 100-page paper offered here - the proof of a 400 year old problem" (ibid).

ALSO INCLUDED IN THE ISSUE ARE PAPERS BY Sigurd B. Angenent, Xavier Tolsa, John B. Etnyre, Ko Honda, Dimitris Achlioptas,, Assaf Naor, Adrian Diaconu, Ye Tian, Antonio Córdoba, Diego Córdoba, Marco A. Fontelos. CONDITION & DETAILS: Complete individual issue in original wrappers. 8vo. Relatively light library stamp on front wrapper, otherwise bright and clean; fine condition inside and out.