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

Preface to the 2004 edition
For this second edition, some minor changes have been made to the initial version,
which was handed in on March 27, 2002 and defended on May 3 the same year. The
changes include a number of corrections of misprints, a revision of the layout and the
figures, and the addition of a name index, a subject index, and a list of boxes. 1 Fur-
thermore, I have included a new preface below, which elaborates on the general theme
of dissertation, namely the analysis of NIELS HENRIK ABEL’S (1802–1829) mathemat-
ics within a transition from formula based to concept based mathematics. This new
“introduction” is an updated and distilled version of the lecture which I gave at the
defence in May 2002.
Funded by grants from the Faculty of Science (Aarhus) and from the Netherlands’
Organization for Scientific Research (NWO), I have continued to elaborate on this
transitional framework, producing two papers focusing on particular aspects such
as critical revision, exceptions, and habituation — processes which are discussed in
the present work. One of these papers is currently accepted for publication in His-
toria Mathematica, (Sørensen, 2005); the other remains in the pipeline and should be
submitted soon. In the future, I will continue to elaborate on the general analytical
framework and its impact on analysing ABEL’S mathematics.
Abel’s mathematics in the context of traditions and
changes
The aim of the dissertation was twofold: to describe and analyse ABEL’S mathematics
within its historical context and to draw perspectives on the general development of
mathematics in the early nineteenth century from the Abelian corpus of mathematics.
The analyses which are drawn from ABEL’S mathematics are — obviously — re-
lated to it, and it has been my main ambition to point to general developments which
shed light on ABEL’S mathematics. That is to say, I do not claim that these trends are
independent of ABEL’S mathematics and could (or should) apply to other periods of
time, other topics of mathematics, or other mathematicians. However, it is my convic-
1 I am grateful for the corrections which were pointed out to me by OLE HALD and by many other
friendly people. However, if some misprints have endured, I would not be too surprised and therefore
beg the forgiveness of the reader.
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