Albert Einstein was a companion of The Doctor renowned as one of the most brilliant scientists of the 20th century.
Biography
Encounters with the Doctor
The Fourth Doctor claimed to have met Einstein. (DW: The Stones of Blood)
In the 1940s, the Rani kidnapped Einstein and brought him to Lakertya so that his genius could be used to help create her Time Brain. (DW: Time and the Rani)
The Eighth Doctor mentioned knowing Einstein. (TN: The Eye of the Tyger)
The Eleventh Doctor once claimed to have had a party at Frank Sinatra's hunting lodge with Einstein and Father Christmas. He produced a photograph of them as proof. (DW: A Christmas Carol)
Other, unspecified, encounters between Einstein and the Doctor included Einstein trying to steal the Doctor's TARDIS, and having his toothbrush taken by the Doctor and 'exterminated' by the Daleks. Einstein also left his bicarbonated processing machine somewhere in the TARDIS.
While working on a malfunctioning time machine of his own in 1945, Einstein was accidentally brought onboard the TARDIS due to an accident involving the TARDIS console and the Doctor's new fez (which Einstein had been the original owner of) along with his fez and a flask of experimental liquid which he hoped was bionic fusion liquid. Einstein was momentarily transformed into an Ood by his liquid, before being changed back and returned home by the Doctor; the mishap had resulted in Einstein's hair standing on end, a look which the Doctor recommended Einstein keep as "more sciencey".(DW: Death Is the Only Answer)
Other references
Sherman thought that Einstein came close to the theory of time travel, but lost it with the "three rivers" theory. (ST: The Way Forwards)
Some compared the child prodigy, Nathan Goss, to Einstein, while others believed his potential exceeded Einstein. (SJA: The Lost Boy)
When Mr Smith was about to self-destruct, Clyde Langer asked Luke Smith what would Einstein do. Rani Chandra reminded Clyde that Einstein "didn't have an alien computer in his room that turns into a bomb". (SJA: Prisoner of the Judoon)
The Eleventh Doctor used Einstein as an example of great people who had dyslexia in order to encourage Elliot Northover to continue trying. (DW: The Hungry Earth)