Really, I don't think INTPs are intelligent as what people of other types would think.
First, they don't have a legitimate specialization (unlike the TJs). Their interest goes everywhere but they're not expected to specialize at anything specific.
But what so good about INTPs is that...where they lack specialization, they compensate pretty much with having a considerable understanding of practically everything.
Biggest area that I think a lot of INTPs have an interest is the humanities. It's speculative, which means it's like an Ne opium or something. Unlike the intelligence required by the corporate working world, for example, where there's too much importance to Te and Si (which I think is just a societal protocol that tells society on what thinking ought to be like), INTPs don't give a damn about that at all that's why they're always able to think outside the box with relative ease more than any archetype.
Having a strong Ti means that any idea produced by the Ne would have a logical framework to it (which is why when an INTP presents an idea, it makes so much sense as compared to other archetypes who don't have a strong Ti).
Having a jacked-up Ne means that they can develop a sense of appreciation for the arts (though being not NF or SP could mean that they may not have that much of an inclination for it), which is something that the working world pretty much ignores.
I've thought that an INTP's NT intellectual competence and their Ne/P (semi artisan) function makes them more intellectually holistic than any archetype, hence the perception that they're smart. But in my opinion, INTPs have just figured out a way to balance the duality.