How intelligent is the Doctor compared to other Galifreyans?

Question

We come across several Daleks in the Whoniverse which the Doctor usually handles completely unarmed and with only his wits. And it's not only 1v1 but he always seems to find a way to handle them, no matter how many there are.

Nonetheless, there was a war between the Daleks and the Galifreyans and the Galifreyans were not able to exterminate the Daleks. This implies that the doctor is way more intelligent / ressourceful than other Galifreyans. This is reinforced by the Doctor being able to handle the Master / Harold Saxon.

So, is the doctor like a Galifreyan genius or how can he outsmart everybody else that should be on his level?

Answer 1

The Doctor's success seems to be a combination of several factors. Intelligence may be one of them. I didn't find it yet, but I remember a conversation he had with the Master about their school days; I believe they were both at the top of their class.

In any case, there is some evidence for him being of high intelligence, but he is not the only one. In "The Deadly Assassin":

ENGIN: It would require a mathematical genius with a phenomenal grasp of applied excitonics.

SPANDRELL: Really? There can't be many of those on the High Council.

and

SPANDRELL: What is the Master like on mathematics?

DOCTOR: He's brilliant, absolutely brilliant. He's almost up to my standard. What's that?

In "The Invasion of Time", Borusa (formerly his teacher), seems to be able to keep up with him, and when let in on the 'secret' inside the lead-shielded room, very quickly comes to understand what the Doctor is about.

Some of the Doctor's success is due to being unpredictable and creative. Even the Master says (in "The Deadly Assassin"),

He remains as ingenious as ever.

In "The Invasion of Time", Borusa and the Doctor discuss some differences in how they think, which is also enlightening:

BORUSA: And you did not think that I could shield myself?

DOCTOR: Well, Lord Borusa, you and the other Time Lords are singularly logical, hmm? You're also short on humour and imagination. You can't offer distractions as I can. What's for tea?

...

DOCTOR: See, you're too single-minded. You're as transparent as good, old fashioned glass.

BORUSA: You're right. I wouldn't last a moment. My mind is too easy to read. The master learns from the student, eh, Doctor?

And some is experience. Most Time Lords are not working in the field. Romana traveled with the Doctor, in part, to learn/benefit from his experience. Many of the Time Lords, though, were simply completely sheltered, and thus unable to deal with many and varied challenges. This is very clear in the episode, "The Invasion of Time".

[Wilderness]

(Leela and Rodan make their way across sand dunes under an orange sky.)

RODAN: Oh, I'm so tired. I must rest.

LEELA: We haven't come far enough.

RODAN: I never thought it'd be like this.

LEELA: What, you've never been outside the Citadel before?

RODAN: No, why should I have? There's everything we need inside.

LEELA: This is much better than inside.

RODAN: It's frightening.

LEELA: Why are you scared?

RODAN: It's all so (pause) natural.

LEELA: We must go on. They can still see us here from the Citadel.

later, by outsider's camp

NESBIN: Protection. Help. You can't survive out here without.

LEELA: I can survive anywhere.

NESBIN: I believe that. What are you?

LEELA: I am a warrior of the Sevateem.

PRESTA: An alien! That's dangerous. Surely they'll come hunting for her?

NESBIN: We'll consider that in a moment. Well, warrior, I don't doubt that you can survive, but what about your friend here?

RODAN: What about me?

NESBIN: Well, you're no alien. I doubt if you've ever set foot outside the Citadel in your life before, have you?

RODAN: No.

NESBIN: Well, out here it's different. You have to fend for yourself.

RODAN: Fend?

NESBIN: That's right. What are you going to eat, for instance?

RODAN: I have some supplies. Look. (Some tablets in a box in her belt pouch.)

NESBIN: They won't last long. When they've gone, what will you do?

RODAN: I, I don't know.

NESBIN: I thought not. You wouldn't even know what you could eat, would you? Have you ever eaten flesh or fruit?

RODAN: No.

NESBIN: And shelter. Do you understand the need for shelter? No, of course you don't. You wouldn't last three days out here.

RODAN: I didn't realise. I'm so tired and cold.

NESBIN: Better get her inside.

NESBIN: Oh, but we are, or rather, we were until we decided to drop out.

LEELA: What is drop out? You fell?

NESBIN: All that peace and eternal tranquillity. We decided to get back to nature out here.

LEELA: Is this true?

RODAN: Well, I've heard it rumoured, but it's a subject that's never mentioned.

NESBIN: Well no, it wouldn't be. Might upset their cosy little world.

Answer 2

I believe all the Time lords are as smart as the Doctor, Romana had shown that she even knew things the Doctor didn't and he was by far older than her... I'm still uncertain but mostly the Doctor is much more adaptive, inventive and certainly possess better creativity than other Time lords who choose to just sit back and observe. There was a part when the Master said the Doctor was failing at the Academy or something (can't remember clearly). He may not be the smartest but he is one of the most powerful, a few times, the Time lords had summoned him, the War Games.. the Time War... both times I believe they were looking for the Timelords most powerful warriors. The Doctor may not be the smartest, but he outwits others because he has experience and a creative drive that isnt common in his race because they choose not to meddle. In fact they have laws against alot of things, of which the Doctor's adventures through space and time had broken hundreds of their law, to fix this he once ran for the Timelords presidency.

Answer 3

There are many different types of intelligence.

In purely academic terms,there are many Academy graduates who got better grades than the Doctor.

Terror of the Autons.

TIME LORD: You are incorrigibly meddlesome, Doctor, but we've always felt that your hearts are in the right places. But be careful. The Master has learnt a great deal since you last met him.
DOCTOR: I refuse to be worried by a renegade like the Master. He's a, he's an unimaginative plodder.
TIME LORD: His degree in cosmic science was of a higher class than yours.
DOCTOR: Yes, well, er, yes, well, I, I was a late developer.

The Ribos Operation.

ROMANA: Very exciting, isn't it?
DOCTOR: Yes, I suppose it must be for someone as young and inexperienced as you are.
ROMANA: I may be inexperienced, but I did graduate from the Academy with a triple first.
DOCTOR: I suppose you think we should be impressed by that, too?
ROMANA: Well, it's better than scraping through with fifty one percent at the second attempt.

But there's much more to it than passing exams. The Doctor's intelligence includes the ability to think on his feet, to improvise solutions, to turn bad situations around, to outsmart the enemy with trickery, and so on. Other Time Lords couldn't do that.