RePoSS #11: The Mathematics of Niels Henrik Abel: Continuation ...

6.9. Reception of ABEL’s work on the quintic 127
it can be developed in radicals, and to declare any equation unsolvable in this way
[by radicals] which does not satisfy the required conditions; from this it follows
as a necessary consequence that the general solution of the equations beyond the
fourth degree is impossible. I invite you to publish this new theory as soon as you
can; it would bring you much honour and generally be regarded as the biggest
discovery remaining to be made in analysis.” 63
The investigations to which LEGENDRE alluded were also described in one of ABEL’S
letters to HOLMBOE, 64 and were partially presented in his notebooks (see chapter 8).
The above citation seems also to indicate that LEGENDRE was unaware of ABEL’S impossibility
proof in CRELLE’S Journal für die reine und angewandte Mathematik 1826. 65
HOLMBOE and the first edition of ABEL’S Œuvres. When the French mathematical
community learned of ABEL’S death in 1829, the Academy sent baron J. F. T. MAU-
RICE. 66 to condole with the Swedish envoy in Paris and suggest that the Swedish
Crown Prince OSCAR undertook the publication of ABEL’S complete works. 67 In 1831,
MAURICE repeated his suggestion and the editorship was delegated to ABEL’S teacher
and friend HOLMBOE and the university in Christiania. 68 By 1836, HOLMBOE had
completed his commentaries on the published works, but intended to include also
selections from ABEL’S unpublished material in the Œuvres. 69 In his report to the
Ministry of Ecclesiastic Affairs 70 in 1838 HOLMBOE declared that — except for a ma-
nuscript which ABEL had handed in to the French Academy 71 — he had finished col-
lecting and commenting upon ABEL’S unpublished works. 72 Two volumes containing
most of ABEL’S published works (with the noticeable exclusion of ABEL’S Parisian
manuscript) 73 and some of the unpublished material from his notebooks and Nach-
lass appeared in 1839. Since most of ABEL’S papers had originally been published
in French and most of his mature entries in the notebooks were in French, it had been
decided that the Œuvres should be in French. An effort was made by HOLMBOE to dis-
63 “Vous m’annoncez, Monsieur, un très beau travail sur les équations algébriques, qui a pour objet
de donner la résolution de toute équation numérique proposée, lorsqu’elle peut être développée en
radicaux, et de déclarer insoluble sous ce rapport, toute équation qui ne satisferait pas aux conditions
exigées; d’où résulte comme conséquence nécessaire que la résolution générale des équations
au delà du quatrième degré, est impossible. Je vous invite à publier le plutôt que vouz pourrez,
cette nouvelle théorie; elle vous fera beaucoup d’honneur, et sera généralement regardée comme
la plus grande dévouverte qui restait à faire dans l’analyse.” (Legendre→Abel, Paris, 1829/01/16.
N. H. Abel, 1902a, 88–89).
64 (Abel→Holmboe, Paris, 1826/10/24. ibid., 44–45).
65 (Holmboe, 1829, 349).
66 (Stubhaug, 1996, 587).
67 After a turbulent period of trembling Danish monarchy and brief independence, Norway was integrated
in the Swedish monarchy 1814.
68 (Ore, 1957, 269)
69 (N. H. Abel, 1902d, 49).
70 As noted in chapter 2, the University was subsumed in the Ministry of Ecclesiastic Affairs.
71 The search for ABEL’S Paris mémoire is a fascinating story in its own right. See (Brun, 1949; Brun,
1953) and section 19.4, below.
72 (N. H. Abel, 1902d, 51).
73 ABEL’S Parisian manuscript known as the Paris mémoire is dealt with extensively in chapter 19.