Nobody feels overly intelligent, except narcissist.

In philosophy there is a term qualia. Qualia are the qualitative properties of experience as defined by the observer, you.

In this way, all people, and all sentient beings feel as if the places they are familiar with, are in some way the center of everything.

My home feels like the home. My thoughts feel like normal thoughts. The people I know feel like normal people.

So in this way, intelligent people feel as smart as anyone does with themselves.

^{“The more I learn, the more I realize how much I don't know.” - Albert Einstein}

One quality all intelligent people have intrinsically, is inquisitiveness; they possess an unrelenting curiosity about the reality around them. A child-like wonder.

A truly capable person possesses a modus operandi, a way of doing things, which enables them to effectively learn. They understand the mechanics of how to understand something.

They see a car, how does a car work? An engine, how does that work? The drivetrain which transfers power from the engine to the wheels, how does that work?

The knowledge of understanding how anything works is simply a byproduct of a willingness, and a desire to understand. With a strong ability to understand, you can learn anything.

Google is the ultimate manifestation of this lesson. You don't need to know everything in the world, you just need to know how to Google.

Many people who consider themselves smart suffer from the Dunning-Kruger Effect. They grossly overestimate their abilities.

“Five percent of the people think; ten percent of the people think they think; and the other eighty-five percent would rather die than think.” - Thomas A. Edison

These people fall into Edison's 10%, they think they smart.

Truly wise people, like Einstein, know that the vastness of all there is to know, in juxtaposition to our capacity to retain knowledge, is humbling and grants a great deal of perspective.

10 percenters are disillusioned in their narcissism, and fundamentally inhibit their ability to continue learning. You may see evidence of this in comments here talking about their loneliness, the lack of perceived intellect in the people around them, and general pessimism.

Cheers.