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

6.9. Reception of ABEL’s work on the quintic 125
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✲ Solvable equations ✛
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Polynomial equations
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Figure 6.1: Limiting the class of solvable equations
be solved algebraically (see section 5.3). Therefore, the class of solvable equations
did not collapse to a few low degree equations; soon, further solvable equations were
found (see chapter 7). The search for a procedure useful in determining whether or
not a given equation could be solved algebraically soon became an interesting project
for mathematical research.
In the following section 6.9, I deal with the first two classes of reactions: the global
and local criticism, which was advanced by ABEL’S contemporaries. In chapter 8, I
describe how ABEL worked on the general problem of solubility, which was realized
to its full extent and attacked shortly afterwards by GALOIS (section 8.5).
6.9 The reception of ABEL’s work on the quintic
When RUFFINI published his proof of the algebraic insolubility of the quintic in Ital-
ian in 1799 the mathematical community of Europe paid little attention. Apart from a
limited Italian discussion involving mathematicians outside the main stream such as
P. ABBATI (1768–1842) and G. F. MALFATTI (1731–1807), only CAUCHY seems to have
taken notice. Twenty-five years later, when ABEL published his proof in a brand new
German mathematical journal, history could have repeated itself. However, ABEL’S
proof soon became widespread knowledge and acquired a status within the math-
ematical community of being rigorous and close to definitive. In this section, I trace
some of the events which played a role in this development, scientific and non-scientific
factors, in order to describe the influence which ABEL’S research had on the subse-
quent evolution of the theory of equations.
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