A genius was someone who demonstrated exceptional intelligence. Coal Hill science teacher Ian Chesterton believed his student Susan Foreman to be a genius. (TV: An Unearthly Child)
The Second Doctor successfully convinced an Ice Warrior to spare his life by claiming to be a genius. (TV: The Seeds of Death)
The Fourth Doctor said that Davros was an "evil genius." Romana II told Sharrel that the Doctor was "an absolute genius" at robotics. (TV: Destiny of the Daleks)
The Tenth Doctor told John Lumic that he would call him a genius "except I'm in the room". (TV: The Age of Steel) He later referred to William Shakespeare as "a genius. The genius." (TV: The Shakespeare Code)