Mail to a friend · Print this article · Previous Columns 
Tony PhillipsTony Phillips' Take on Math in the Media
A monthly survey of math news

This month's topics:

Sphere packing in the New Scientist

Jacob Aron's report, published online on August 12, 2014, bears the title "Proof confirmed of 400-year-old fruit-stacking problem." The problem: Johannes Kepler's conjecture that "no packing of congruent balls in Euclidean 3-space has density greater than the face-centered cubic packing" (this quote from the Flyspeck Project completion report, released on August 10). As Aron puts it, "The problem is a puzzle familiar to greengrocers everywhere: what is the best way to stack a collection of spherical objects, such as a display of oranges for sale? In 1611 Kepler suggested that a pyramid arrangement was the most efficient, but couldn't prove it." Thomas Hales (U. of Pittsburgh) "broke the problem down into ... thousands of possible sphere arrangements ... and used software to check them all." He submitted the proof to the Annals of Mathematics in 1998. "But the proof was a 300-page monster that took 12 reviewers four years to check for errors. Even when it was published ... in 2005, the reviewers could say only that they were '99 per cent certain' the proof was correct." This was not enough for Hales. His Flyspeck Project, started in 2003, "used two formal proof software assistants ... both of which are built on a small kernel of logic that has been intensely scrutinised for any errors -- this provides a foundation which ensures the computer can check any series of logical statements to confirm they are true." And now: "On Sunday, the Flyspeck team announced they had finally translated the dense mathematics of Hale's proof into computerised form, and verified that it is indeed correct."

The Flyspeck completion report gives a sample of mathematical text and how it appears translated into machine-digestible logical notation:

Aron widens the context: "A computer-verified proof of a 400-year-old problem could pave the way for a new era of mathematics, in which machines do the grunt work and leave humans free for deeper thinking."

2014 Fields Medals in the media

The 2014 Fields Medals, awarded in August at the ICM in Seoul, received unusually prominent international coverage principally because, for the first time, one of the four prizes went to a woman: the Iranian mathematician Maryam Mirzakhani (Stanford). The other medalists were Artur Avila (IMPA, CNRS-Jussieu), Manjul Bhargava (Princeton) and Martin Hairer (Warwick).

Putting more math into common discourse

Last May 24, the Slate web magazine posted an installment of Mike Pesca's daily news and culture podcast "The Gist," that includes an interview with Jordan Ellenberg (starts at about 8:35). Ellenberg recently published "How Not To Be Wrong." After some initial badinage about people's seeming pride in their mathematical ineptitude, about the Laffer curve ("you can explain it to a Congressman in six minutes and he can talk about it for six months") and about some faulty applications of linear regression, Pesca asks Ellenberg what he hopes to achieve with his book. "I'd like to see some of the deep ideas of math, ideas which are part of our cultural heritage, that people have hammered out over many centuries of hard work, I'd like to make a world where it is safe and accepted and customary to talk in that language. Not in a book that's declared as a math book, not in a magazine that's declared as a science magazine, but in a regular editorial in the New York Times, or a regular article in a magazine, or a regular piece on Slate. In the same way that it's no longer considered weird or technical to talk about the incentives people face: that language has moved out of the academy and people have seen how useful it is. I think there's space for more of mathematics to get out there as well."

Tony Phillips
Stony Brook University
tony at math.sunysb.edu