Solving Quintics and Mathematical Quandaries

I believe some, but not all, quintic equations are algebraically solvable. Fermat's Last Theorem has been proven I think. And a list of many unsolved problems can be found at http://mathworld.wolfram.com/topics/UnsolvedProblems.html

Where's the proof?

Here's a blurb at the same site about Fermat's Last Theorem.

http://mathworld.wolfram.com/FermatsLastTheorem.html

I had a good friend that attended the week long lecture series by Wiles in London. She told me it was obivious something big was developing and suddenly exotic maths lectures given during the week started getting very full of very serious, heavyweight mathematicans. On the final Friday of his lecture series showed how the general proof of the Taniyama-Shimura conjecture excluded other conjectures from being true, and wrapped up with "and of course this consequentially proves by contradiction Fermat's last theorem" - there was stunned silence then the full of sober Professors stood and cheered and burst out in praise for the man who had solved a millennium problem that took 153 years to prove!