The Koide formula was discovered by Japanese theoretical physicist Yoshio Koide in 1981.
It provides a relatively simple mathematical relationship for the masses of the Electron, Muon and Tau particles - and was later modified and extended to Neutrinos, Quarks and other particles.
Experimental measurements show that the formula is accurate (at low energies) - but to date no-one can explain why.
The formula states :
$${\displaystyle Q={\frac {\;m_{e}+m_{\mu }+m_{\tau }\;}{\left(\,{\sqrt {m_{e}\,}}+{\sqrt {m_{\mu }\,}}+{\sqrt {m_{\tau }\,}}\,\right)^{2}}}=0.666661(7)\approx {\frac {\,2\,}{3}}~,}$$
( me is the electron mass, mμ is the muon mass, and mτ is the tau mass.)
The mass relationships are unexplained - with seemingly arbitrary numbers leading to a very simple fraction.
Further technical reading, see : arXiv from Piotr ̇Zenczykowski, of the Henryk Niewodniczanski Institute of Nuclear Physics, Poland.
Note: Not all particle physicists agree on the significance of the formula - maintaining that it's just a mathematical co-incidence.