Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

From what I've studied, Abel-Ruffini theorem states that we can't find all the roots of some polynomials with degree above 5, using only radicals and arithmetic operations.

How does it imply that we can't have a formula that involves some other mathematics thus allowing us to find all the roots of any polynomial? Do abstract algebra and Galois theory have a role in this I'm not aware of?

share|cite|improve this question
It does not, actually. We can construct solutions of quintics using mathematical function, yes. Lame way to do this : $f(a)$ where $f(x)$ is defined to be the inverse function of $x^5 + x$. This is the "so-called" bring radical. Smart way to do this : Elliptic functions. Explicitly given here. – Balarka Sen May 9 '14 at 19:48
up vote 3 down vote accepted

It doesn't imply there isn't some other formula. Hermite, for example, found a solution for the general quintic using theta functions.

share|cite|improve this answer
Could you explain better? – mattecapu Apr 29 '14 at 17:34
Not much, I'm afraid. I don't actually know how it was done, only that it was. Wikipedia has something here: There are some sources linked in this discussion:… – jdc Apr 29 '14 at 17:37
Probably It would be too complex for me to understand it now. Thank you! – mattecapu Apr 29 '14 at 17:57

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.