mat

The root mat- only makes sense once you take it apart inside one Greek word: automatos. The Greeks built it from auto- ('self') and a second piece, -matos, tied to the idea of mind, will, or inner drive (the same family that gives Greek menos, 'spirit, urge'). So automatos literally described something that acts of its own will — a thing that moves because it wants to, not because a hand pushes it.

For the Greeks this was almost magical: a door that swings open on its own, a temple gadget that pours water without anyone touching it. The word carried a sense of wonder — motion with no visible cause, as if the object had a will inside it.

English borrowed this idea and froze it into a small, tight family. Strip auto- off and you are left with -mat-, the 'self-willed' core:

- auto- (self) + mat + -ic (adjective) -> automatic: acting by itself, no human needed
- auto- + mat + -ate (to make) -> automate: to give a process that self-acting quality
- auto- + mat + -ion (act, state) -> automation: the state of running by itself

Notice that mat- never appears alone in English. It always rides behind auto-, because the whole concept is 'self + driven.' That is also why the meaning has stayed so stable: from an ancient self-opening temple door to a modern self-driving factory line, every member of the family is about a thing that runs on its own will.

One caution worth flagging, because the spelling is a trap. Three common words look like they belong here but do not: mate (a Germanic word for companion), mature (from Latin maturus, 'ripe, timely'), and stigma (Greek for a 'mark' or 'tattoo'). None share the automatos source. Treat mat- as a one-family root: if the word is not about something acting by itself, it is not this mat-.