Question: A friend of mine asked me if I could explain this statement: "It's not logically possible to prove that something can't be done". The actual reason is the understanding of this strip: 

![enter image description here](https://i.stack.imgur.com/YtHMp.gif)

Since I'm not an expert on logic, but at least know the basics, I told him that the statement is false. To prove it I gave him the counterexample of the impossibility of trisecting an angle by using only straightedge and compass, which was proved by Pierre Wantzel. This shows clearly that it's possible to prove that something can't be done.

When I told him this, he explained to me that this is sort of naive because Asok, the guy who makes the statement, is a graduate from IIT and also I read that he's always a brilliant character in the strip. 

Can you guys please tell me what you think about this? Also I'd like to know how you would interpret this dialog.

Answer: 
It's a paradox: by saying "it's not logically possible to do X", Asok is, in effect, claiming that there must exist a *proof* that X is impossible. Which is impossible, if Asok is right.

Hence Asok must be wrong!
To put it simply, it is considered illogical to say that something will *never* happen.