Some twenty five years ago I read a book that, to this day, still sticks in my mind.
The story (spoiler alert) is called Ender's Game involves a small child in a future world named Ender. Ender is selected by the "government" as a gifted child capable of helping the "earth" defend itself from the "buggers."
The future earth is not a nice place and the buggers (insectoid life forms) are coming to ruin it further.
Ender is recruited into the service where he is trained in various forms of 3D strategy (space battles being fought in 3D).
Much of Ender's trainings involve what basically amounts to a very realistic video game.
As the story progresses it is revealed that the "video game" is actually a real time, faster-than-light transmitter called the ansible which allows the player to view and control remote spaceships in actual battles with the buggers.
The story was written by Orson Scott Card in the mid 1980's.
Since that time a number of sequels and other related things have appeared.
From a geek perspective this is a fascinating stroke of vision on the part of Card.
Remember that this predates internet, remote controlled drones, the martian lander, and so on.
Today this book is used by the military for strategy. Ender was a clever child and figured many strategies out to escape the "buggers."
I have often wondered about the concept of placing a problem, say some sort of mathematical problem, into a game where "winning" the game means solving the problem. Of course the solution would not be in the game - instead there would be a prover that would run to decide if the problem was solved.
Players would "contribute" to the solution via game play - for example developing strategies that the game would remember. The game could, over time, integrate these strategies into the gameplay allowing later users to build on what earlier players learned.
These ideas are not wild speculation.
Recently a protein folding problem was resolved in this way: see this.