Thomas Royen discovered the solution to the Gaussian Correlation Inequality Conjecture, a problem that had unhinged mathematicians for more than 60 years.

Professor Royen, in an image provided by his institution.

The retirement It can be the best gift or the worst nightmare of a worker, whatever the area.

With it, they receive the just rest they deserve after so many years of joys and sorrows at work, but many feel empty due to the drastic change that their day-to-day undergoes, and they are not able to completely abandon what was their job.

But in this case they do it without the stress of yesteryear and that is why they are often able to solve problems that they were unable to fix throughout their working lives.

This is precisely the case of Thomas Royen, a German statistician from 67 years that in 2014 he managed to solve a problem that it had not only been impossible for him, but had brought hundreds of mathematicians upside down since it was enunciated, more than 60 years.

His case has recently been narrated in Quanta Magazine and the most curious thing is that everything happened in a most common way: while Royen was brushing his teeth.

Fix problems in the bathroom

Many musicians claim to compose their songs in the bathroom, having the ideal acoustics for it.

Perhaps it also awakens the mind, because it was precisely there that Thomas Royen was brushing his teeth when what seemed to be the solution to the conjecture of Gaussian Correlation Inequality, an easily understandable mathematical problem, but so difficult to explain that it had driven a great number of mathematicians crazy in the last decades.

This problem states that if they overlap two figures, such as a rectangle and a circle, and darts are thrown at them, the probability that these will land on the union of both will be equal to or greater than the probability that it will hit the ends of the rectangle multiplied by the probability that it will hit the the circle individually.

It is relatively easy to visualize, but explaining why has been the subject of study for many mathematicians, who have ended up retiring without getting any answers. But retirement is not the end, as Royen has shown, who saw the answer very clearly one day, while brushing his teeth at home.

He immediately wrote his conclusions in Microsoft Word, writing an article that later would send both to the platform arXiv like a series of mathematicians from different universities, who as soon as they received it knew that the problem was finally solved.

It had been many years of research through complicated formulas, which finally ended when someone, already retired from his profession, decided to look for the simplest of explanations.

And it is that, in science, many times the solution to the problems is so simple that it hides mockingly in front of the noses of the investigators; until, one day, a whirlwind of foam and toothpaste gives them the solution.