|Would you like a jelly baby?|
THEORY 1: He's human
He could be a man who simply looks like a previous incarnation of the Doctor - hence why the Eleventh Doctor says "I never forget a face." After all, we've seen a Pompeian who looks like the Twelfth Doctor (Caecilius in "The Fires of Pompei") and a Timelord who looks like the Sixth Doctor (Commander Maxil in "The Arc of Infinity"). So, it's not inconceivable that an ordinary human could look like an older, prior incarnation of the Doctor. This makes the most logical sense, but it doesn't entirely explain away the curator's apparent knowledge of events that have happened in "The Day of the Doctor". It's also the least interesting theory.
THEORY 2: He's the Fourth Doctor
The effect of saving Gallifrey has massively changed the Doctor's own timeline, such that his fourth incarnation did not die when he fell from the communications tower in "Logopolis". Instead, his fourth self went on to lead a long life, ending up as a curator at the National Gallery. This explains why he looks so much older in "The Day of the Doctor". Of course, this means he is a past Doctor, which makes it difficult to explain how he knows who Matt Smith is. There's also a whole host of questions surrounding what else may have changed in the Doctor's past. For my money, this is the most interesting theory.
THEORY 3: He's the Future Doctor
The Doctor, in some long-distant future incarnation, decides to regenerate into a body that looks like his fourth incarnation. This is entirely possible - perhaps he had a fondness for that body? Tom Baker was, after all, the longest serving TV Doctor. We also know there is technology out there (thank you, Sisterhood of Karn) that allows a Timelord to choose what they look like when they regenerate. There is prior form for this as well: when Romana (a Gallifreyan companion of the Fourth Doctor) regenerated, she chose to look like Princess Astra, a woman she had met in "The Armageddon Factor". This would explain how the curator knows who the Eleventh Doctor is, knows about the events of "The Day of the Doctor" and suggests that the Doctor will eventually become a curator, just as the Eleventh Doctor had pondered.
THEORY 4: He's Tom Baker
This was just a bit of fan service from Steven Moffat, and nothing should be read into it.
What do you think...?