Professor

Professor was a title given to scholarly teachers to denote their academic ability. It was often, though not exclusively, given to those who had achieved a certain level of learning of held a position that earned them the title.

Ace often referred to the Seventh Doctor as "the Professor" throughout her early association with him (TV: Dragonfire) and still continued to refer to him as 'professor' in a friendly manner several years later. (PROSE: Happy Endings) This may have been in reference to the fictional character Professor X.

References

In the year 100,000,000,000,000, Yana was given the title of professor, despite there having been no universities for over a century. (TV: Utopia)

Professor Marius, who built K9 and later gave him to the Fourth Doctor, was a specialist in extraterrestrial pathological endomorphisms (alien viruses) at the Bi-Al Foundation in the year 5000. (TV: The Invisible Enemy)

Bernice Summerfield originally faked her qualifications as a professor of archaeology; however she did eventually obtain a professorship. (PROSE: Love and War, Return of the Living Dad)

Professor Candy interviewed River Song when she applied to Luna University to study archaeology. (TV: Let's Kill Hitler)

River Song introduced herself to the Tenth Doctor as a professor of archaeology. She was not yet a professor at the time of the crash of the Byzantium. (TV: Silence in the Library, The Time of Angels)

The crew of the Russian submarine that the Eleventh Doctor encountered in 1983 called Grisenko the Professor. (TV: Cold War)