It’s a problem that the world’s most experienced mathematicians have spent decades trying to solve, and the solution had eluded them at every turn – the infamous Gaussian correlation inequality (GCI).

Then, out of nowhere, a retired German statistician figured out the proof while hunched over the sink, cleaning his teeth. But rather than being celebrated by the wider mathematical community, the proof went largely ignored. Because how could such an unlikely figure have outsmarted them all?

“I know of people who worked on it for 40 years,” Donald Richards, a statistician from Pennsylvania State University, told Natalie Wolchover at *Quanta Magazine*. “I myself worked on it for 30 years.”

First proposed in the 1950s, but properly formulated in 1972, the GCI principle sounds relatively simple:

If two shapes overlap, such as a rectangle and a circle, the probability of hitting one of those overlapping shapes – say, with a dart – increases the chances of also hitting the other.

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