Proofs of obscure provenance are sometimes overlooked, but if they're published in the right place, the good ones eventually are recognized. A problem exists when publication takes place elsewhere. Here's a case of something interesting and useful that was somehow discovered anyway -- the Gaussian correlation inequality.

snip

...

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.

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.”

Royen hadn’t given the Gaussian correlation inequality much thought before the “raw idea” for how to prove it came to him over the bathroom sink. Formerly an employee of a pharmaceutical company, he had moved on to a small technical university in Bingen, Germany, in 1985 in order to have more time to improve the statistical formulas that he and other industry statisticians used to make sense of drug-trial data. In July 2014, still at work on his formulas as a 67-year-old retiree, Royen found that the GCI could be extended into a statement about statistical distributions he had long specialized in. On the morning of the 17th, he saw how to calculate a key derivative for this extended GCI that unlocked the proof. “The evening of this day, my first draft of the proof was written,” he said.

...