I am trying to understand Arnold's proof for the insolvability of the quintic from the manuscript:


which is actually well written. However, I am stumbling in Page 4 where the author says "By contrast, Exercise 1 implies that any combination of the four field operations, continuous functions, and a single nesting of radicals would produce a loop." and the subsequent Proposition 6.

Where does the single nesting of radicals come in Exercise 1? There is no nesting of radicals mentioned before this statement. Can anyone help? Thanks.


1 Answer 1


In Exercise 1, take $\alpha = 1/3$, say. That's a cube root, ie a single nested radical.


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