Magnetic monopoles
Magnetic monopoles are hypothetical magnets with only one pole in contrast to "conventional" magnets that have two.
Some fields of theoretical physics, such as string theory, require magnetic monopoles, although their existence has not be proven so far. For further information refer to wikipedia.
Sheldon submitted a grant proposal to prove the existence of slow moving magnetic monopoles to the National Science Foundation, which sends him and the other three guys on an expedition to the North Pole (0223). During that expedition, Sheldon thought he discovered evidence of the hypothetical particles, thereby proving string theory, only to discover that his data had been altered by the other guys to keep him from behaving like a "dictator" (0301).