A Long-Sought Proof, Found and Almost Lost

Thomas Royen who solved the Gaussian correlation inequality (CGI)

Thomas Royen at his home in Schwalbach am Taunus, Germany.

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.

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.
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