Retiree Discovers Elusive Math Proof

I like this because is shows that retirees make real discoveries.  And recall hearing about this challenge long ago, it has real use.  Problem is well described in the paper, but is math-technical.  In Wired: 

A Retiree Discovers an Elusive Math Proof—And Nobody Notices
As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of geometry, probability theory, and statistics that had eluded top experts for decades.

Original story reprinted with permission from Quanta Magazine .... 

Known as the Gaussian correlation inequality (GCI), the conjecture originated in the 1950s, was posed in its most elegant form in 1972 and has held mathematicians in its thrall ever since. “I know of people who worked on it for 40 years,” said Donald Richards, a statistician at Pennsylvania State University. “I myself worked on it for 30 years.”  ....  "