Mathematicians are just discovering that a major breakthrough in the field of geometry and probability was found and published in 2014 by a retired German statistician.
Sometimes the answer is just under your nose. Literally.
In 2014, 67-year-old Thomas Royen had a moment of clarity while was brushing his teeth. The solution to a probability problem that had stumped mathematicians since the 1950s was, suddenly, so simple!
“In mathematics, it occurs frequently that a seemingly difficult special problem can be solved by answering a more general question,” said Royen, according to the Independent.
The solution that Royen had stumbled upon was the mathematical proof of the Gaussian correlation inequality (GCI). It can be stated in general terms as such: If you place two different shapes on top of one another while playing a game of darts, the chances of hitting one shape increases the chances of hitting the other.
It was known to be true, but no one could prove it.
Except for Royen! Having long worked as a statistician, he was not a career mathematician. Instead, his interest in the GCI was based around creating better statistical models of the results of studies conducted by pharmaceutical companies.
Royen excitedly typed out the solution in Microsoft Word, and, without much fanfare, published his findings on the academic site arvix.org. However, most mathematicians use a professional software called LaTeX instead of Word, and false solutions to the GCI were common. Thus, many experts were skeptical of his solution.
But not mathematician Donald Richards from Pennsylvania State University, who had worked on the GCI problem for 30 years.
“When I looked at it I knew instantly that it was solved,” he said. “I really kicked myself.”
However, many others were still doubtful that Royen had solved it.
According to the Independent, Royen sent all of his research materials and a paper to Bo’az Klartag, a mathematician at the Weitzmann University of Science in Tel Aviv. However, because Royen’s paper was bundled with other research, some of which contained mistakes, Professor Klartag threw the entire bundle away. Royen’s research was then mostly forgotten for two years before the academic community began to take notice, especially since, as a retiree, he had no desire to endure the long and difficult process of submitting his findings to a peer reviewed publication.
The slow trek of progress marches on, however, and slowly but surely, his solution gained greater and greater attention. Royen, humble as ever, was simply grateful to make a difference.
“It is like a kind of grace. We can work for a long time on a problem and suddenly an angel—[which] stands here poetically for the mysteries of our neurons—brings a good idea,” Royen said.