@vzn (Einstein to Kaluza on combining GR and EM in 5D, from Zee's GR):
"February 27, 1925: More than 3 years later, Einstein wrote: "I am still of the opinion that your idea... is of great originality and merits the serious interest of academic colleagues... . I myself have so far struggled with this problem in vain. It often appears to me that the magnetic field of the earth is based upon an as yet unknown connection between gravitation and electromagnetism, but I cannot come out of the inconsistencies." To a present-day theoretical physicist such as myself, that last sentence sounds rathe…

The ultimate way/trick to remember the positions
$$[M_{\mu \nu},M_{\rho \sigma}] = i (M_{\mu} \, ^{ \nu} \eta^{\rho \sigma } + M_{\mu} \, ^{\nu} \eta^{\rho \sigma} - M_{\nu} \, ^{\mu} \eta^{\rho \sigma} - M_{\nu} \, ^{\mu} \eta^{\rho \sigma}) $$
$$= i (M_{\mu \sigma} \, ^{\nu} \eta^{\rho \sigma}_{\nu \rho} - M_{\mu \rho} \, ^{\nu} \eta^{\rho \sigma}_{\nu \sigma} - M_{\nu \sigma} \, ^{\mu} \eta^{\rho \sigma}_{\mu \rho} + M_{\nu \rho} \, ^{\mu} \eta^{\rho \sigma}_{\mu \sigma})
$$
$$= i (M_{\mu \sigma} \eta_{\nu \rho} - M_{\mu \rho} \eta_{\nu \sigma} - M_{\nu \sigma} \eta_{\mu \rho} + M_{\nu …