> I have a student writing a paper on Abel's proof of the insolvability of
> fifth and higher degree polynomial equations by radicals. Abel's two
> papers on this are in French. While that's no problem for me, it is for
> my student! Does anyone know if these have been translated into English
> by anyone? I don't have the time to make translations for my student.
>
> Thanks,
> David Pengelley
>
> David Pengelley (davidp@nmsu.edu)
> Mathematics, New Mexico State University, Las Cruces, NM 88003 USA
> Tel: 505-646-3901=dept., 505-646-2723=my office; Fax: 505-646-1064
While not answering your question, the following may be of relevance.
I am currently building up a collection of papers by Sir William
Rowan Hamilton, on the Web, in TeX format. A number of papers
(including the major papers on Dynamics, some optics-related
material, papers and letters relating to the discovery and early
work on quaternions, and some of the papers on the Theory of
Equations) have been available, in preliminary versions, for about
a year or more. I am currently preparing the major optics papers
(the 'Theory of Systems of Rays' and its three supplements), and
also some of the later papers (including 'On Fluctuating Functions',
'On Symbolical Geometry', and 'On Geometrical Nets in Space'); and
I hope to make these available on the Web in a few months time when
I have completed the work of proof reading and editing. The URL
for Hamilton-related material in my 'History of Mathematics' website
is
http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/
One of those papers (which has been available for about a year) is
Hamilton's detailed exposition of Abel's proof:
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.
Hamilton discusses the proof of Abel, in very great detail, and
supplies his own correction to a portion of Abel's proof that
he considers incorrect or incomplete. (It seemed to me a year
ago that there was a small gap in a part of Hamilton's version
of the proof, though that could be fixed up using the methods
and results described by Hamilton; I cannot remember the details
now, though I believe that I would be able to identify the problem
were I to go back and study the paper in detail again.) The URL
for this paper is
http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/Quintic/
The paper is in English!
(This paper is also included in the third volume of the Royal Irish
Academy edition of Hamilton's mathematical papers. In my edition,
I have corrected a number of obvious typographical errors overlooked
by the editors of that edition, some of which are noted in handwritten
corrections in a reprint of that paper, donated by Hamilton himself
to our College library. I have also corrected some misprints
introduced into the Royal Irish Academy's edition. Of course I
have no idea how many typos I have myself introduced into my own
edition! Any corrections would be most welcome.)
I hope to transcribe Abel's original papers some day, and make them
available on the Web (linked to the Hamilton pages). However this
is only one of many such tasks that I have not yet found time to
undertake.
David Wilkins
dwilkins@maths.tcd.ie