Inventing a new product, service, or system
Finding something of significance that was lost (the Ark of the Covenant, the lost city of Atlantis, etc.)
Discovering a new species in the natural world
Discovering a hidden civilization
Creating something that solves a major problem (the cure for cancer, technology for keeping personal data secure online, an educational system that ensures the success of every child, kitty litter that turns poo into a renewable energy source, etc.)

There are five basic human needs that, when missing from a character's life, could motivate them to pursue this goal. The following needs are all possibilities, but only one of them should be the primary driver for any given character. For more information on the relationship between human needs and outer motivations, please see this Character Motivation tutorial.

Self-Actualization: If the creative drive is strong enough, along with one's need to express oneself in that way, this goal could be something the character is motivated to pursue.
Esteem and Recognition: To elevate himself in the eyes of others, a character might strive to make himself stand out via this means.
Love and Belonging: If a loved one is suffering and the character has the ability to come up with a way to stop it, he may be driven to create or discover the solution.
Safety and Security: If the character's personal security is at stake, he may find himself pursuing this goal as a way of getting back to a place of safety.