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Can 5th order equations be solved by means other than radicals?

  1. May 19, 2012 #1
    As the title suggests, we know from the Abel-Rufini theorem that 5th order equations cannot be solved using radicals. I haven't managed however to find an either positive or negative answer to the following statement:

    "Can 5th order equations be analytically solved by means other than radicals?"

    This of course rules out numerical solutions. It is pretty contrary to my intuition, however I am entertaining the notion in case it can be solved using modern (or exotic :tongue:) mathematics that are not yet easily found in books.

    Any ideas mathematicians? :biggrin:
  2. jcsd
  3. May 20, 2012 #2

    Stephen Tashi

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    Science Advisor

    In a history of math book that I read as a teenager, I recall that Hermite produced a non-algebraic solution. So I just now went searching for it on the web, and I think it is this:
    http://en.wikipedia.org/wiki/Bring_radical See the section on The Hermite–Kronecker–Brioschi characterization. I haven't studied this material.
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