Sisyphean describes a task that is endless, a task that is impossible to complete. The term Sisyphean is derived from the Greek myth concerning Sisyphus. The god Hades punished Sisyphus for his hubris and deceitfulness by condemning him to eternally roll a boulder uphill, never reaching the top of the hill before the boulder mysteriously rolled itself back down the hill, an endless task that was impossible to complete. The word Sisyphean was first used in the middle 1600s.
Herculean describes a task that is very difficult and requires great strength of mind or body, and courage. The term Herculean is derived from the Greek myth concerning Heracles, in which Heracles had to complete twelve labors in order to atone for killing his wife and children. The name Heracles was Romanized as Hercules. The word Herculean was first used in the late 1500s.
Promethean means innovative, rebelliously creative, bold. The word Promethean is derived from the Greek myth concerning Prometheus. According to the story, Zeus withheld the gift of fire from humanity. Prometheus took pity on humanity, stole fire from Mount Olympus and brought it to the world. The word Promethean was first used in the late 1500s. The terms Sisyphean, Herculean and Promethean are all derived from proper names, and are therefore properly rendered as capitalized.
Examples
Cleveland is a resurgent city, but one seldom perceived that way, because surges here are so Sisyphean. (The Atlantic)
While it’s nice to think that we can just come up with a big idea and iterate, adapt and pivot our way to success, at the heart of any serious transformation is people like James Allison and his colleagues, who spend years of Sisyphean labor, quietly figuring things out. (Forbes Magazine)
Surely, to defeat Umno/Barisan Nasional is a Herculean task, it was so even with a single Opposition entity like Pakatan Rakyat. (Free Malaysia Today)
Gone are the Herculean schedules of his prime, a concession to the fact that his body does not recover as quickly as it once did. (The Baltimore Sun)
Done economically, that would be a Promethean achievement, representing a huge step toward solving the two outstanding challenges in shifting from fossil fuels to renewable energy: storing large amounts of energy for later use, and powering forms of transportation that cannot easily run on batteries. (MIT Technology Review)
But it turns out that the great majority of billionaires, far from being the Promethean geniuses celebrated by Mises and Rand, are a lot more like turtles on fenceposts. (The Augusta Free Press)