Right let's clear this up. There is even a website dedicated to it. So read the answer and let's continue talking about farts and space!
From here
You see, the AOAT confusion all arises from misses - misconceptions, misinterpretations, and misunderstandings. Consider three rewordings of the question:
1) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I begin to attempt to take flight in the plane, and you attempt to match my speed to try to keep me stationary. Will the plane take off?
2) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I throttle up the airplane and you turn on the treadmill, and we conspire by our joint effort to try to keep the plane stationary relative to the ground. Will the plane take off?
3) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I attempt to take flight in the plane, but you match my speed with the treadmill and keep me stationary relative to the ground. Will the plane take off?
Here are the absolute, 100%, bet-your-life-on-it answers to these rewordings:
Yes.
No.
Whoever asked this question is an idiot.
And that's about all this debate comes down to, folks. If we could all agree on one set of rules for the thought experiment, then we ought to be able to make the explanation of the answer clear. As it stands, normally one side has interpretation (1) in mind, and argues vehemently with someone else who has interpretation (2) in mind, and the whole thing blows up into a senseless squabble.
Here are the three core facts that are rock-solid:
A) If the plane remains stationary relative to the ground, it will not take off.
B) If the plane moves relative to the ground, it will take off.
C) The person operating the conveyor belt cannot by himself make the plane remain stationary relative to the ground.
From here