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: 
I think what the author means is that it is impossible to prove that a software "will never work": you can observe it isn't working by now. But does that mean it will ever work? (excluding trivial scenarios in which the software cease to exist, etc). I think he kind of wants to get in the impossibility of proving absolute existence or absolute nonexistence. Just my thoughts on it... Having said that, your argument about Wantzel seems to be right, just not what the author was pointing out.
To put it simply, it is considered illogical to say that something will *never* happen.