Allah created the mountains stable to stabilise the earth and prevent it from moving and shaking
Question

does the Quran and sunnahever say or mention that mountains are inmoving or unshakable? Because I study geology and we know mountains move with the movement of tectonic plates but it is very small and unnoticed by humans. Also if Quran and sunnah never say this why do so many mufaseereen and scholars say this?
Praise be to Allah.Firstly: 
The Holy Qur’an speaks of the mountains and explains that Allah, may He be exalted, created them so as to make the earth stable and, so that it would not shake or move. 
Allah, may He be exalted, says (interpretation of the meaning):
“And the earth We spread out, and placed therein firm mountains”
[al-Hijr 15:19]
“And We have placed on the earth firm mountains, lest it should shake with them”
[al-Anbiya’ 21:31]
“Have We not made the earth as a bed,
And the mountains as pegs?”
[an-Naba’ 78:6-7]
“And the mountains He has fixed firmly”
[an-Naazi‘aat 79:32]. 
The description of the mountains as “firm” and the statement that Allah, may He be exalted, “fixed them firmly” means that they are stable. This is reflected by the meaning of the root of these words in Arabic.
See: al-Qaamoos al- Muheet (p. 1662); Lisaan al-‘Arab (14/321) 
This idea of the mountains being firmly fixed is not denied by geology. Geological research proves that the mountains are fixed firmly in the earth and that they stabilise the earth. The roots of the mountains beneath the surface of the earth are several times deeper than the height of that which appears above the surface. 
Hence Allah, may He be exalted, stated that He made the mountains pegs, and the part of the peg that is driven into the ground is longer than the part that remains above it. That is what gives it greater strength so that it can hold firm the ropes of the tent. 
With regard to what geology says about the mountains moving horizontally a few millimetres every year, and that they are moving vertically, increasing or decreasing in height by a few millimetres every year, these are theories that do not contradict the description of the mountains as being stable and fixed, because it is a very slight movement that cannot be noted except by means of very precise instruments, and the effects of that movement appears after millions of years. 
That is what they say, and Allah knows best how true it is; there is no reference to that in the apparent meanings of the Qur’an. 
Secondly: 
One of the texts we will quote here is the verse in which Allah, may He be exalted, says (interpretation of the meaning):
“And you will see the mountains and think them solid, but they shall pass away as the passing away of the clouds. The Work of Allah, Who perfected all things, verily! He is Well-Acquainted with what you do”
[an-Naml 27:88]. 
Some contemporary scholars are of the view that what is referred to here is the spinning of the earth on its axis and that when the earth spins, the mountains spin with it. 
But this view is not correct. Rather the correct view about the meaning of this verse is that it is speaking about the Day of Resurrection, when Allah will blast and scatter the mountains and move them from their places. This is indicated by the context of the verses, as this passage is speaking about the Day of Resurrection. 
Moreover, the other verses that speak about the moving of the mountains all speak about the Day of Resurrection. Allah, may He be exalted, says (interpretation of the meaning):
“And (remember) the Day on which the Trumpet will be blown and all who are in the heavens and all who are on the earth, will be terrified except him whom Allah will (exempt). And all shall come to Him humbled.
And you will see the mountains and think them solid, but they shall pass away as the passing away of the clouds. The Work of Allah, Who perfected all things, verily! He is Well-Acquainted with what you do”
[an-Naml 27:87-88]. 
The commentator Shaykh Muhammad al-Ameen ash-Shinqeeti (may Allah have mercy on him) said: The words of Allah, may He be exalted, “And you will see the mountains” follow on from the words “And (remember) the Day on which the Trumpet will be blown and all who are in the heavens and all who are on the earth, will be terrified…” That is: (remember) the Day on which the Trumpet will be blown and all who are in the heavens will be terrified and you will see the mountains… The context clearly indicates that the passing away of the mountains that will be like the passing away of the clouds will occur on the Day on which the Trumpet will be blown; it is not happening now. End quote. 
He also said: 
All the verses which speak of the mountains moving refer to the Day of Resurrection, such as the verses in which Allah, may He be exalted, says (interpretation of the meaning):
“On the Day when the heaven will shake with a dreadful shaking,
And the mountains will move away with a (horrible) movement”
[at-Toor 52:9-10]
“And (remember) the Day We shall cause the mountains to pass away (like clouds of dust), and you will see the earth as a levelled plain”
[al-Kahf 18:47]
“And the mountains shall be moved away from their places and they will be as if they were a mirage”
[an-Naba’ 78:20]
“And when the mountains shall made to pass away”
[at-Takweer 81:3].
End quote from Adwa’ al-Bayaan (6/490) 
Ibn Katheer (may Allah have mercy on him) said:
The words “And you will see the mountains and think them solid, but they shall pass away as the passing away of the clouds” [an-Naml 27: 88] mean: you see them as if they are fixed and will remain as they are, but they will pass away as the clouds pass away; that is, they will move from their places, as Allah, may He be exalted, says (interpretation of the meaning):
“On the Day when the heaven will shake with a dreadful shaking,
And the mountains will move away with a (horrible) movement”
[at-Toor 52:9-10]
“And they ask you concerning the mountains, say; ‘My Lord will blast them and scatter them as particles of dust.
‘Then He shall leave it as a level smooth plain.
‘You will see therein nothing crooked or curved’”
[Ta-Ha 20:105]
“And (remember) the Day We shall cause the mountains to pass away (like clouds of dust), and you will see the earth as a levelled plain”
[al-Kahf 18:47].
End quote from Tafseer Ibn Katheer (6/217) 
Conclusion: there is nothing in the Qur’an that refers to the movement of the mountains during the life of this world. 
For more information please see:
http://www.alukah.net/culture/0/63837/
https://www.alukah.net/sharia/0/72873/
And Allah knows best.