The Secret Life of Numbers: 50 Easy Pieces on How Mathematicians Work and Think (2006)
Chapter: References
References
7
TWINS, COUSINS, AND SEXY PRIMES
Dan Goldston and Cem Yildirim, “Small gaps between consecutive primes,” http://aimath.org/primegaps/goldston_tech.
Andrew Granville and K. Soundararajan, “On the error in Goldston and Yildirimi’s ‘Small gaps between consecutive primes’,” http://aimath.org/primegaps/residueerror/.
9
THE TILE LAYER’S EFFICIENCY PROBLEM
Tom Hales, “The honeycomb conjecture,” Discrete and Computational Geometry, vol. 25 (2001), pp. 1–22.
10
THE CATALANIAN RABBI’S PROBLEM
Preda Mihailescu, “Primary units and a proof of Catalan’s conjecture,” Journal für die reine and angewandte Mathematik, forthcoming; “A class number free criterion for Catalan’s conjecture,” Journal of Number Theory, vol. 99 (2003), pp. 225–231.
13
HAS POINCARÉ’S CONJECTURE FINALLY BEEN SOLVED?
Grisha Perelman, “The entropy formula for the Ricci flow and its geometric applications,” DG/0211159, “Ricci flow with surgery on three-manifolds,” DG/0303109, and “Finite extinction time for the solution to the Ricci flow on certain three-manifolds,” DG/0307245, http://arXiv.org.
18
GOD’S GIFT TO SCIENCE?
Stephen Wolfram, A New Kind of Science, Wolfram Media, Inc., Champaign, Ill., 2002.
23
KNOTS AND TANGLES WITH REAL ROPES
Yuanan Diao, “The lower bounds of the lengths of thick knots,” Journal of Knot Theory and Its Ramifications, vol. 12 (2003), pp. 1–16.
Burkhard Polster, “What is the best way to lace your shoes?,” Nature, vol. 420 (2002), p. 476.
25
IGNORANT GAMBLERS
“The communication of risk,” Journal of the Royal Statistical Society: Statistics in Society, vol. 166 (2003), pp. 203–270.
26
TETRIS IS HARD
Erik D. Demaine, Susan Hohenberger, and David Liben-Nowell, “Tetris is hard, even to approximate,” http://www.arxiv.org/PS_cache/cs/pdf/0210/0210020.pdf.
33
HOW CAN ONE BE SURE IT’S PRIME?
Manindra Agrawal, Nitin Saxena, and Neeraj Kayal, “PRIMES is in P,” http://www.cse.iitk.ac.in/news/primality.html.
34
A MATHEMATICIAN JUDGES THE JUDGES
Lawrence Sirovich, “A pattern analysis of the second Rehnquist U.S. Supreme Court,” Proceedings of the National Academy of Sciences, vol. 100 (2002), pp. 7432–7437.
37
COMPRESSING THE DIVINE COMEDY
D. Benedetto, E. Caglioti, and V. Loreto, “Language trees and zipping,” Physical Review Letters, vol. 88 (2002), p. 48702.
38
NATURE’S FUNDAMENTAL FORMULA
Johan Gielis, “A generic geometric transformation that unifies a wide range of natural and abstract shapes,” American Journal of Botany, vol. 90 (2003), pp. 333–338.
40
THE FRACTAL DIMENSION OF ISRAEL’S SECURITY BARRIER
B. B. Mandelbrot, “How long is the coast of Great Britain? Statistical self-similarity and fractal dimension,” Science, vol. 155 (1967), pp. 636–638.
G. Dieter and Y-C. Zhang, “Fractal aspects of the Swiss landscape,” Physica A, vol. 191 (1992), pp. 213–219.
41
CALCULATED IN COLD ICE
Naohisa Ogawa and Yoshinori Furukawa, “Surface instabilities and icicles,” Physical Review E, vol. 66 (2002), p. 41202.
43
BUZZING AROUND CORNERS
S. Fry, R. Sayaman, and M. H. Dickinson, “The aerodynamics of free-flight maneuvers in Drosophila,” Science, vol. 300 (2003), pp. 495–498.
44
INEXPERIENCED TRADERS MAKE THE MARKET EFFICIENT
John List, “Testing neoclassical competitive market theory in the field,” Proceedings of the National Academy of Sciences, vol. 99 (2002), pp. 15827–15830.
45
THE WAGGLE DANCE OF INTERNET SERVERS
Sunil Nakrani and Craig Tovey, “On honey bees and dynamic allocation in an Internet server colony,” Proceedings of 2nd International Workshop of Mathematics and Algorithms of Social Insects, Atlanta, Ga., 2003.
47
ENCRYPTING MESSAGES WITH CANDLES AND HOT PLATES
Norbert Hungerbühler and Michael Struwe, “A one-way function from thermodynamics and applications to cryptography,” Elemente der Mathematik, vol. 58 (2003), pp. 1–16.
49
INSULTS STINK
Alan G. Sanfey, James K. Killing, Jessica A. Aronson, Leigh E. Nystrom, and Jonathan D. Cohen, “The neural basis of economic decision-making in the ultimatum game,” Science, vol. 300 (2003), pp. 1755–1758.
50
BIBLE CODES: THE NOT SO FINAL REPORT
Robert Aumann and Hillel Furstenberg, “Findings of the Committee to Investigate the Gans-Inbal Results on Equidistant Letter Sequences in Genesis,” Center for Rationality, Discussion Paper 364, June 2004, http://www.ratio.huji.ac.il/dp.asp.
