During what was an unremarkable summertime ’s morning , a 67 - yr - older valet de chambre had a modern - day constantan minute , allowing him to suddenly crack a chance job that has mix up mathematical statistician since the 1950s .
Quanta Magazinerecently reported the story ofan unassuming sack out German mathematical statistician call Thomas Royen , who came up with a mathematical validation for the Gaussian correlation inequality ( GCI ) during a brief flash of inspiration while brush his tooth in July 2014 .
The GCI principle is all about geometry and probability . It was first suggest in the 1950s and more eloquently formulated in 1972 . Although unco simple to understand , it has evade numerical explanation .
Here ’s an example of how it works : think you are throwing darts at a target made up of any two convex symmetrical shapes that are centre on the same point . More simply put , a target made up a rectangle with a round cold shoulder - out put down over the top of it . The phone number of flit that bump off the circle , rectangle , or both will come out in a normal bell - curve distribution , known as a Gaussian emplacement , with the majority of the darts hitting in the overlapping section .
GCI articulate that the probability of a flit slay the convergence is always adequate to or high than the individual chance of it landing inside the rectangle procreate by the private probability of landing in the roofy . This makes common sense , but it has proved to be a pain to explain mathematically .
“ I know of mass who exploit on it for 40 year , ” Donald Richards , a mathematical statistician at Pennsylvania State University , toldQuanta Magazine . “ I myself worked on it for 30 years . ”
Royen , however , found a remarkably satiny answer to it . The same solar day he had his eureka import , he typed up the calculations on Microsoft Word ( as he did n’t be intimate how to habituate the fancy Good Book central processor used by professional mathematicians ) and sent the paperto the pre - print websitearXiv . The paper is called “ A simple proof of the Gaussian correlation speculation . " He sent the solution to a few statisticians in the US who he cerebrate might be interested .
“ I got this clause by email from him , ” I. A. Richards lend . “ And when I reckon at it I knew instantly that it was solved . ”
His work has gone more or less unrecognized in the field . However , that ’s for the most part due to Royen ’s relaxed mental attitude towards the whole result , choosing to avoid the foresightful and arduous match - review system of rules . With no career to judge and promote , he ’s just well-chosen that the proof is now ground .
