Shaking gin is a poor substitute for not having gin at the right temperature (cold enough). It is emergency CPR to resuscitate a dead martini. Much of the flavour of gin is the result of oxygen content (dissolved oxygen in the gin). Keeping it in the freezer does this naturally. Shaking with ice also does it, however there is also a "metallic" aftertaste sometimes, so shaking does alter other flavours and isn't the preferred method. At least this has been my life experience, though I've never done a survey about it. The King Cole Room does count as a bastion of martini lore in NYC, even if they didn't invent it.