Throughout the Dr. Who series, the doctors have claimed to be hundreds, even thousands of years old, (the tenth and eleventh both claim to be around 900, but throughout the series, eleven jumps into the thousands, even though its only been a few years for his companions, and now the 12th claims to be 2,000) but in relation to what? He is constantly jumping around through time, making it difficult to track. Does he claim his age to be in relation to Gallifrey as if he hadn't left or it hadn't been burned, (or saved, it's all too timey-wimey for me to make sense of) or does he simply not know?
Welcome to Doctor Who - full of inconsistencies.
This question is discussed here. Here's the theory subscribed to by the executive producer and scriptwriter:
"He has no clue"
A simple and self-evident theory is that the Doctor doesn't know how old he is because he has lost count, constantly travelling backward and forward through time making it difficult to measure one's lifespan at all. This theory began as fanon, with the Doctor occasionally admitting to being unsure of his age in spinoff media (COMIC: Doctor Who and the Time Witch, PROSE: Vampire Science); eventually it became solidified as canon in a televised story. (TV: The Day of the Doctor), although the War Doctor's immediate response suggesting he was 400 years younger than the Eleventh complicates matters.
This is the theory subscribed to by Doctor Who's current 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." - Steven Moffat, SFX, May 2010