Gaussian correlation inequality (GCI) conjecture is considered to be the world’s most complex geometry and probability problem that has left scores of mathematicians scratching their heads for an answer. But this retired German mathematician has solved the problem while he brushed his teeth.

Thomas Royen, 67, from Schwalbach am Taunus, near Frankfurt first solved the problem in 2014 while brushing his teeth,

Thomas’ GCI solution went largely unnoticed for the last few years, but it is slowly starting to be recognized amongst the mathematical community, reports Quanta Magazine.

The problem first arose in the 1950s and was redefined in 1972, with thousands of mathematicians being unsuccessful in attempting to solve it.

The GCI problem says that if two shapes overlap, for example, a rectangle and a circle, the probability of hitting one, as in a game of darts, will also increase the chances of hitting the other. Mr. Royen solved the GCI conjecture by analytically explaining it through statistical formulas, which led to a surprisingly simplified function and solution.

Mr. Royen said:

‘In mathematics, it occurs frequently that a seemingly difficult special problem can be solved by answering a more general question. The evening of this day, my first draft of the proof was written.’

The solution has been compiled in a paper called ‘A simple proof of the Gaussian correlation conjecture,’ and only employs classic mathematical techniques.

Mr. Royen added,

‘I hope that the surprisingly simple proof…might encourage young students to use their own creativity to find new mathematical theorems. A very high theoretical level is not always required.’

He added:

‘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.’

Kudos my good sir!