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

items published in the same year are separated by letters. There are a few exceptions
to these rules — mainly concerning ABEL’S publications. All collected works and a
few other items have been given more illustrative names, e.g. (N. H. Abel, 1839; N.
H. Abel, 1902e) which denote the first edition of ABEL’S Œuvres and the Norwegian
Festschrift of 1902, respectively. Some of ABEL’S manuscripts have been dated and
published posthumously; for these, the year they were written is included in brackets
as in (N. H. Abel, [1828] 1839). References to ABEL’S manuscripts and notebooks are
of the form (Abel, MS:351:A). Letters are refered to as (Abel→Holmboe, Kjøbenhavn,
1823/06/15. In N. H. Abel, 1902a, 3–4), which denotes the letter from ABEL to B. M.
HOLMBOE (1795–1850) sent from Copenhagen on June 15, 1823. I have only used
published letters, and the references are given.
Mathematics and notation. It has been my general ambition to unwrap and disen-
tangle the mathematics presented in the dissertation to such a degree that the reader
who holds no particular knowledge of the topics discussed but is familiar with math-
ematical reasoning and mathematical notation should be able to benefit from the ar-
guments and analyses. At the same time, it has been a high priority of mine to present
the mathematics produced in the early nineteenth century in a way which respects and
represents the way its creators thought about it. However, I have introduced a mini-
mum of notational advances, in particular combining sums into the modern notation
using the summation sign. I have also occasionally renumbered indices or replaced
symbols to ease the notation. Throughout, I write Σn for the symmetric group on n
symbols, which is elsewhere frequently referred to as Sn. Slightly off-topic mathemat-
ical themes have been placed in boxes shaded gray.
Names and portraits. Upon first mention, historical actors are listed with their full
Christian names and years of birth and death according to the Dictionary of Scientific
Biography. 2 In situations where the person is not included in the Dictionary of Scien-
tific Biography, other sources are employed and explicitly referred to. 3 Full names and
dates of important persons are sometimes repeated in various parts. Unless other-
wise noticed, all pictures stem from the history of mathematics internet archives at St.
Andrews, Scotland. 4
Acknowledgments
My utmost gratitude extends towards my supervisor, KIRSTI ANDERSEN. For more
than four years, KIRSTI has always kindly guided me and put up with my chang-
ing moods. KIRSTI has read most of the chapters of the present dissertation while
2 (Gillispie, 1970–80).
3 Mostly (Biermann, 1988; Poggendorff, 1965; Stubhaug, 1996).
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