Why are some extremely smart people very quiet, and how do you know that they are smart?

How can the ‘Smart People’ be called ‘Smart’ if they let others figure out the cause of their silence? So, Mr. Noufal Ali, the first part of your Question remains  a ‘MYSTERY’.

Coming to the second part of your Query, I would like to say that they are SMART because:

1. They are UNIQUE in terms of their COMMUNICATION STYLE.
2.  Their absence RATTLES us.
3.  We miss their PAR EXCELLENCE LIVELY DISCUSSIONS.
4. Without them, the whole SCENARIO is covered by a SMOKE SCREEN.
5. We feel as if something is MISSING from our LIVES.
6. All the YUMMINESS of our discussions is LOST, and,
7.  We miss the LOVELY/MAGICAL COMMENTS made by them.

One of the reasons might be that most of the conversations going around are pointless, time and energy consuming and non-value added. 

We notice how smart they are in critical situations and brain stimulating conversations and in the way they intruduce their ideas to the table. 

I agree with  Farhana Siddique Fari Answer

Intelligent people tend to appear quiet because they are natural observers. They are listening and watching what's going on around them. They tend to analyze the situation, breaking it down into parts like a social puzzle, and ask themselves questions to figure it out.

If smart person do not know a topic very well he would be quiet, while the extroverts would just make random comments and guesses about the topic. But if he knew the topic well, he would be able to explain it concisely and refute false ideas logically. Because his statement were fewer but more accurate, he thought people assumed he was smart than he was.

But that may not be true. A person who is talking is only stating what they have thought and are not gaining new knowledge. A person who is listening or reading is learning.

The difficulty comes for introverts when they realize the person talking does not know as much as they do. A co-worker once asked why I would not share my information much in a meeting. The extroverts would just start talking, parroting what they had heard earlier and then move on to ideas that obviously wouldn't work. It was too late to present my ideas which countered theirs without insulting them.

The other difficulty is that when I thought an idea through I was confident about it and did not ask for consensus, which the extroverts felt they had the right to weigh in on. This is probably because they realized their own ideas were half-formed and needed refinement. They assumed everybody presented ideas in that manner.

Because they knew a gentle answer turns away wrath,   but a harsh word stirs up anger.

The tongue of the wise adorns knowledge,    but the mouth of the fool gushes folly. Therefore smart only knows another smart.

Thanks

I support the answer which given by Mrs. Farhana

Some major signs of smart people which i have seen are: 

1. They strive for perfection

2. They like to stay updated

3. They are constantly occupied with works

4. They stay up late night

If a person is smart then the reason behind his smartness is quietness. He thinks before he speaks. His words are his actions. He try to convince people by his words not actions.

              And according to the question hoe you can know a person is smart, the answer is in he question. Their quietness is the main tool to recognize that a person is smart and mature.

             These type of people are straight-forward thats why other people miss them and their comments.

Not to argue with the question, but I think that some extremely smart people can be very outgoing and talkative as well - and I think that has to do with both setting and personality (which some people have already said) and the example about some/most US presidents having an above average IQ but also being completely comfortable standing on stage giving speeches and talking to crowds is a good one