Koide Formula

In my opinion this is one of the most interesting but simple mysteries in modern physics. Anyone can understand it, but so far no one can explain it!

If you take the masses of the three known leptons, (the electron, the muon, and the tau) which are the seemingly random numbers 0.511 MeV, 105.7 MeV, and 1777 MeV, sum the masses , and then divide by the square of the sum of the square roots of the masses, the result is equal to 2/3 accurate to less than ~0.01% !

And the mystery gets more interesting still. Consider the most extreme cases: If all three lepton masses are exactly equal, the result would be exactly 1/3. If one lepton is very heavy and the other two are very light, then the result is very close to 1. The measured value of 2/3 falls exactly halfway between the two!

This clearly suggests some underlying theory, but in 25 years no one has found it. And this relation does not seem to apply to any other set of particles.