What is the Doomsday algorithm?

A mental method, invented by John Conway, for finding the day of the week of any date in the Gregorian calendar — in your head, in seconds.

Give it any date — a birthday, a historical event, a date in 2087 — and it returns Monday, Tuesday, and so on, with no lookup and no memorised calendar. It rests on one clever anchor: each year has a special weekday (its "doomsday") that a set of easy dates always fall on, so every other date is a short count away. It's the classic "what day were you born?" party trick.