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

378 Chapter 19. The Paris memoir
As described, ABEL’S deductions in the Paris memoir were extremely cumbersome
and not always universally permitted. Generally, ABEL’S arguments in the memoir fell
well inside the formula based paradigm: they were concerned with formulae, were car-
ried by manipulations of formulae, and arguments which were not universally true
but only true “in general” were acceptable. In chapter 21, these features will be shown
to be intimately connected with an “old” paradigm which was gradually being re-
placed in the period. Thus, and because it was not available for 15 years, it is not
surprising to find that ABEL’S proof in the Paris memoir was not so widely accepted
and imitated as the statements or results to which they led.