The very first thief to emerge on the Disc. He stole the secret of fire from the Gods and, even though he got his fingers burnt on the deal and it was hard to fence, is revered even today by Thieves everywhere.
The story is explored further in The Last Hero, where we learn that the Gods, out of respect for his audacity and because they are sentimental about some things, granted Fingers immortality. But because the Gods are also just, and because they wanted make a VERY big point about what happens to people who dare steal things from Dunmanifestin, they decreed that he spend his immortality trapped in a place found on no map, chained to a rock, where once a day a very big eagle flies down and pecks his liver out. (It is assumed that the liver regenerates overnight).
Mazda was eventually freed by Cohen and the Silver Horde, who took it in turns to shake him reverentially by the hand, gifted him a very big sharp sword, and departed. That eagle is in for something of a surprise... as is the Discworld, now its first and greatest thief is free again - and immortal, with a self-regenerating body to boot...
Bears more than a passing resemblance to the Greek legend of Prometheus, which shares many characteristics with the tale of "Fingers" Mazda...
In Zoroastrianism (incidentally the birth religion of Queen singer Freddie Mercury) Ahura Mazda is the creator and highest divinity, whose visible presence in the world is manifested through fire.
Strauss' Also Sprach Zarathustra, known better as the music from 2001 - A Space Odyssey, is an attempt to recapture the moment the light of Mazda was born into the world.
Artist Maxfield Parrish painted a calendar series for the Edison Mazda Lamp Division in the 1920s. They were extremely popular and widely distributed. One of the paintings features Prometheus stealing fire, with the words “Edison Mazda” at the top. `Prometheus'