I made Hamilton's exposition (and small correction) of Abel's proof
available on the Web some time ago. The URL for Hamilton's paper
On the Argument of Abel, respecting the Impossibility of
expressing a Root of any General Equation above the Fourth
Degree, by any finite Combination of Radicals and Rational
Functions.
is
http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/Quintic/
I am very grateful for notification of any typographical or other
errors that people notice in the material available from this site.
The above paper is included in an expanding collection of resources
relating to Sir William Rowan Hamilton that I am building up at
http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/
(I have already made available the text of about thirty of
Hamilton's mathematical papers, and in recent months have been
preparing for release on the Web some of Hamilton's more
substantial papers on quaternions, including the quaternion
papers in the Philsophical Magazine, further papers on the Theory
of Equations (with his refutation of Badano's supposed method of
solving quintic equations by radicals), and also his paper on
'Algebraic Couples', with the 'Essay on Algebra as the Science of
Pure Time'. I hope to release this on the Web in the coming
months.)
(I would also like to make Abel's original paper on the quintic
available some time in the future, when I can find the time to type
it up.)
Yours,
David Wilkins,
Trinity College, Dublin.
>
> Dear Colleagues,
>
> Many thanks for the extremely helpful messages you posted in response to my
> earlier question about the history of the concept of function. I am very
> grateful. Perhaps you can also help me with another query.
>
> I am looking for material that will help render more intelligible Abel's
> famous proof (1824) of the general insolubility in radicals of quintic
> equations. I am a physicist, rather than a mathematician, and have been
> working with some colleagues here to study his 1824 paper and see if his
> arguments can be made more transparent without having recourse to the later
> abstract vocabulary of Galois theory (I do know the fine works of Hadlock
> and the Maxfields in this vein). Can any of you direct me to writings that
> clarify either the history immediately preceding his work? Even more, how
> one should assess its significance in relation to the issue of
> transcendental and algebraic numbers and as a mathematical watershed
> comparable to the ancient discovery of irrationality?
>
> I appreciate your generous help.
>
> Sincerely,
>
> Peter Pesic
> St. John's College
> Santa Fe, NM USA