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 et al) and still continued to refer to him as 'professor' in a friendly manner several years later. (PROSE: Happy Endings)

Ace possibly did so 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.

River Song introduced herself to the Tenth Doctor as a professor of archaeology. (TV: Silence in the Library)