Sometimes mathematics challenges come from the oddest places....and sometimes their solution is attached to a great amount of money. An example is the "Netflix Challenge", with an attached prize of $1,000,000.
Some background: To help its 7-million customers find the "best-preferred" movies, Netflix developed Cinematch, an in-house movie recommendation system whose merit is based on its ability to mathematically "predict whether someone will enjoy a movie based on how much they liked or disliked other movies." In October 2006, Netflix announced the challenge, with the prize going to the person/group that creates a recommendation (based on a mathematical algorithm) that is at least 10% better than Cinematch.
The Challenge will continue through "at least" October 2, 2011. Netflix received 169 entries within 2 weeks of announcing the contest, with three entries being slightly better than Cinematch. After a month, approximately one thousand algorithms had been entered...but the best was an 8.43% improvement by an AT&T team.
Now, almost two years later, 37721 contestants on 30918 teams from 173 different countries have entered the challenge. You can follow the progress of the Challenge by checking the "Leaderboard". When I last checked, the current leader was The Ensemble Experts, a team of investment data miners (i.e. making useful sense out of gigantic sets of data). Their score: an 8.841% improvement via their mathematical algorithm.
Join in...watch the fun as diverse people (and individuals such as "Just a guy in a garage") use sophisticated mathematics to tweak their algorithms.
Source: Adapted from Jordan Ellenberg's "The Netflix Challenge," Wired, March 2008, pp. 114-122