The Doctor's age
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This is the theory subscribed to by Doctor Who executive producer and head writer Steven Moffat in an interview with SFX:
The thing I keep banging on about is that he doesn't know what age he is. He's lying. How could he know, unless he's marking it on a wall? He could be 8,000 years old, he could be a million. He has no clue. The calendar will give him no clues.
This theory would be voiced in The Day of the Doctor, written by Steven Moffat, when the Eleventh Doctor is asked by the War Doctor how old he is now.
Non-fictional sources
The first non-fictional writing about regeneration, The Phoenix in the TARDIS, stated that the First Doctor was about 900 at the time he regenerated into the Second Doctor.
Invalid sources
An incarnation of the Doctor who featured in Introduction to the Night gave his age as 700 years old while refering to himself in the third person.
