Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"In Math, Computers Don't Lie. Or Do They?" by Kenneth Chang. The New York Times, 6 April 2004.
"The Math Guy: Pyramids and Oranges," Keith Devlin. Weekend Edition, 10 April 2004.
"Journal juggles balls to publish Kepler proof," News in Brief,
Nature, 15 April 2004, page 686.
"Irrwege eines mathematischen Beweises: Kontroverse um die Rolle des Computers in der Mathematik," by George Szpiro. Neue Zuercher Zeitung, 21 April 2004.

The Annals of Mathematics will soon publish Thomas Hales's proof of the Kepler Conjecture, a statement about the most efficient way to pack spheres. The Annals is not publishing the proof's computer sections, however; they will be published in Discrete and Computational Geometry. Referees have been checking the entire proof, hundreds of pages long, for years but although they found no mistakes, they can not be completely sure that all the computer calculations in the proof are correct---thus, the proof is being split. In Chang's article, Robert MacPherson, an Annals of Mathematics editor, says the part of Hales's proof being published in the Annals has been verified and "We feel that he [Hales] has made a serious contribution to mathematics." Several mathematicians are quoted in the article, which gives background on Kepler's Conjecture and attempts at proving it. The article also contains a discussion of the role of computers in proofs. Chang writes, "Dr. Hales said that final publication, after a review process originally expected to last a few months, would be almost anticlimactic. 'For me, the big moment was when I completed the proof... and I don't think anything will change when I see it in print.'"

Devlin, in an interview with National Public Radio's Linda Wertheimer, also discusses the conjecture and its proof---pointing out how sphere-packing is connected to data-packing---and reveals that he received "a bag of hate mail" after writing an article on the changing nature of proof.

--- Mike Breen