The Kepler Conjecture: The Hales-Ferguson Proof
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The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work. Thomas C. Hales , Mellon Professor of Mathematics at the University of Pittsburgh, began his efforts to solve the Kepler conjecture before He is a pioneer in the use of computer proof techniques, and he continues work on a formal proof of the Kepler conjecture as the aim of the Flyspeck Project F, P and K standing for Formal Proof of Kepler.
Samuel P. Ferguson completed his doctorate in under the direction of Hales at the University of Michigan.
In , Ferguson began to work with Hales and made significant contributions to the proof of the Kepler conjecture. His doctoral work established one crucial case of the proof, which appeared as a singly authored paper in the detailed proof.
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Jeffrey C. He is a pioneer in the use of computer proof techniques, and he continues work on a formal proof of the Kepler Conjecture as the aim of the Flyspeck Project F, P and K standing for Formal Proof of Kepler.
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In , Ferguson began to work with Hales and made significant contributions to the proof of the Kepler Conjecture. Read more Read less. From the Back Cover The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in by Johannes Kepler and mentioned by Hilbert in his famous problem list. About the Author Thomas C. No customer reviews.
Mathematicians deliver formal proof of Kepler Conjecture
They were thus led to wonder whether for some given force field there would be some optimal function whose bound exactly matched the energy of the E8 or Leech lattice. This is reminiscent of the uncertainty principle of quantum theory — the more one tries to pin down the position, the more difficult it is to pin down its momentum since, in quantum theory, the Fourier transform of position is momentum.
In the case of dimension 8 or 24, Viazovska conjectured that these restrictions limited any magic function to the border of possibility — any additional restrictions, and no such function could exist; any fewer, and such a function would not be unique. Thomas Hales, who proved the Kepler conjecture, was very impressed with this result, saying that even in light of the earlier work, I would not have expected this [universal optimality proof] to be possible to do.
Sylvia Serfaty, a mathematician at New York University, described the work as at the level of the big 19th-century mathematics breakthroughs. Some additional details are given in this well-written Quanta Magazine article , also by Erica Klarreich, from which some of the discussion above was adapted. The new joint paper is available here. Math Scholar Mathematics, computing and modern science Comments Posts. Optimal stacking of oranges.
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May 17th, Category: Essays. Recent Posts. Math Scholar Mathematics, computing and modern science. Comments Posts. Sphere packing in higher dimensions Mathematicians have been investigating similar sphere packing problems in higher dimensions for many years.
Scientists Deliver Formal Proof of Famous Kepler Conjecture
Credit: Wikimedia and Jgmoxness Viazovska proved that the E8 lattice is the most efficient sphere-packing result for 8 dimensions. E8 is a remarkable structure, beautifully illustrated in the graphic at the right. It is a Lie group of dimension , and is unique among simple compact Lie groups in having these four properties : a trivial center, compact, simply connected and simply laced i.
In , researchers affiliated with the American Institute of Mathematics succeeded in calculating the inner structure of E8 in a large supercomputer calculation. Magic functions It is now three years since the E8 and Leech lattice papers. May 17th, Category: Essays Comments are closed. Recent Posts New paper proves year-old approximation conjecture How many habitable exoplanets are there, really?