Is the method used in Abel's impossibility theorem completely algebraic?

Question

I need a little help. I am looking for answers to these questions.

1) Can you give me a direct PDF resource for read Abel's impossibility theorem (not Abel-Ruffini theorem) ? I can not find. In Wolfram Mathworld I found only this information:

" In general, polynomial equations higher than fourth degree are incapable of algebraic solution in terms of a finite number of additions, subtractions, multiplications, divisions, and root extractions. This was also shown by Ruffini in 1813 (Wells 1986, p. 59) ".

2) What is the difference between Abel's theorem and Abel Ruffini's theorem?

3) Is the method used in Abel's theorem completely algebraic? Do I need to have strong high math knowledge to understand the theorem?

P.S. Maybe everybody knows the answer to these questions. Since I have not a math teacher, I had to ask these questions in MSE. I may not have picked the tags correctly.

Thank you.

Answer 1

You have already been told in the comments that the Abel-Ruffini theorem and Abel's impossibility thorem are the same thing. Concerning the proof of the theorem, it is purely algebraic and it doesn't require deep algebra. Of course, it does not use Galois theory, since it had not yet been created. I suggest that you read these articles:

• Niels Hendrik Abel and equations of the fifth degree, by Michael I. Rosen;
• Abel and the unsolvability of the quintic, by Jim Brown.