Why does the Angel win in the problem of the Angel and the Devil (game theory)?

Question

Mathematics

It is obvious that the Devil can build a wall around the Angel (which is tied to the starting position), you just need to build the wall as far, with a margin, at a distance more than k-moves, that the Angel would need to approach it.
Is there a problem in the mathematical notation or the requirements for "correct proofs"? Because logically there are no problems (for me and my imagination, even if we are dealing with infinity).
Perhaps it's all about the limitations of mathematical syntax?
I would be glad if you explain what is the general complexity of this problem and why mathematicians since 1982 have not been able to close the question.
ps Unfortunately, I don't have a mathematical background. There is only good imagination and logic from programming, so of course I argue from my own bell tower.

Answer 1

Where does the assumption that "the Angel wins" come from?
If the strength of the angel is 1, then the devil has a winning strategy.
What does tied to the starting position mean?
IMHO, in the general case (k > 1) your strategy loses, since the angel will get to the border of the circle faster than the devil will build the wall.

Answer 2

Perhaps the whole point is in the limitations of mathematical syntax?

definitely not limited. When it was necessary to extract an even root from -1, they made a checkmate machine
https://www.youtube.com/watch?v=sxiKlOK3EJY
pi.math.cornell.edu/~numb3rs/psamuelson2009/5_23_a...
And here is the strategy for winning an angel
The Angel of power 2 wins
Andras Mathe
homepages.warwick.ac.uk/~masibe/angel-mathe.pdf
You can read strategies for the devil in Conway