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The "time brain" was a giant brain created by the Rani. By using the minds of geniuses from across time and space, the Rani planned to use the brain to do the calculations needed to create a Time Manipulator with which she could reshape the universe to her liking. One of the items on her agenda was to revert Earth to the age of the dinosaurs so that they could realise their full potential. Her plans were stopped when the Seventh Doctors' brain was added, stopping the Rani from controlling it because she hadn't taken into account the Doctor's erratic nature.
Individuals used to create the Time Brain included Albert Einstein, Louis Pasteur, and Hypatia. (TV: Time and the Rani)
Behind the scenes
In the Children in Need sketch Dimensions in Time, the Seventh Doctor uses the term "time brain" to describe the brain of a Time Lord.