Math Will Rock Your World

"A generation ago, quants turned finance upside down. Now they’re mapping out ad campaigns and building new businesses from mountains of personal data"

"Neal Goldman is a math entrepreneur. He works on Wall Street, where numbers rule. But he’s focusing his analytic tools on a different realm altogether: the world of words."

"Goldman’s startup, Inform Technologies LLC, is a robotic librarian. Every day it combs through thousands of press articles and blog posts in English. It reads them and groups them with related pieces. Inform doesn’t do this work alphabetically or by keywords. It uses algorithms to analyze each article by its language and context. It then sends customized news feeds to its users, who also exist in Inform’s system as — you guessed it — math."

Read full article:
http://www.businessweek.com/magazine/content/06_04/b3968001.htm

Sphere Packing Problem

In 1611, after having studies how sailors stack cannonballs, Johannes Kepler began pondering over the most efficient way to pack spheres in a given space. He finally decided on the face-centred cubic, which is the same way you will find oranges stacked today.

However, Kepler could not prove that the face-centered cubic was indeed the most efficient way to pack spheres. Until recently this problem remained unsolved. After over a decade of research, testing all the possible solutions, Thomas Hales of the University of Michigan concluded that Kepler’s method, the face-centred cubic, was indeed the most efficient way to stack spheres, meaning that the amount of space occupied by the spheres is maximized in the proposed arrangement. Referees have declared they are 99 percent sure the Hale’s solution is correct.

http://www.simonsingh.net/Sphere_Packing.html