192 Normat 56:4, 192 (2008)
Summary in English
Nils Baas and Christian Skau, Sel-
bergintervjuet IV - IAS and Obiter
Dicta (Norwegian).
In the final part of the interview Sel-
berg reminiscences about colleagues at
the Institute of Advanced Study, where
he spent almost all of his professional
life. In particular Selberg recalls Ein-
stein, Gödel, Oppenheimer, Nash and
in particular Hermann Weyl for whom
he entertained a very high regard, as
well as some of the conflicts that ra-
ged at the Institute. He presents his
views on mathematics, upholding the
Platonic view that mathematicians do
discover objective phenomena indepen-
dent of man, and that mathematical for-
malism never can fully encompass the
workings of the mathematicians mind,
thus dismissing Hilberts project as a
failure. Furthermore he discusses the
great Norwegian mathematicians and
explains why he finds Riemann so much
superior to Weierstrass. He reflects on
what characterizes good mathematics
and the future of mathematics, in parti-
cular its relation to applications. In par-
ticular he emphasizes that simplicity is
very fundamental to mathematics not
only aesthetically, and this is why Weyl
was far more important than say Siegel.
He reveals his preferred working met-
hods, admits that he never uses compu-
ters, not even for e-mail. In the end he
is asked about religious beliefs, if any,
hobbies, and taste in literature. Finally
he singles out the trace formula as his
most important mathematical achieve-
ment.
Jan Boman, Datortomgrafins mate-
matik (Swedish).
Computerized tomography is a very im-
portant diagnostic tool in modern medi-
cine. Mathematically it boils down to
reconstructing a function f(x, y) from
its integrals
R
L
fds over each line in the
plane. This problem was solved already
in 1917 by the Austrian mathematici-
an Johann Radon, who gave an expli-
cit expression for the function f . The
lines in the plane are usefully seen as
points in the so called dual plane, and
the function
ˆ
f(L) =
R
L
fds is nowadays
referred to as the Radon transform (of
f). Radon thus gave a mathematical-
ly beautiful inversion of this transform.
The applications of Radons work are
not restrained to medicine (where Ra-
don’s results were rediscovered in the
60’s) but include geology, especially ses-
miology and oil-prospecting, and many
other industrial and commercial enter-
prises. In the article an elementary and
detailed account of the reconstruction
is presented using Fourier transforms
and convolutions, allowing a numerical
simulation (invaluable to any applica-
tion).
Olav B. Skaar, Generalisering av det
gylne rektangel til høyere dimensjoner
(Norwegian).
In this article a generalization of the gol-
den mean is presented, differing from an
earlier one suggested by Huntley in the
60’s. While the classical golden mean is
given by the relation
a
1
+a
2
a
1
=
a
1
a
2
= φ
2
for cutting a given segment (a
1
+ a
2
)
into two a
1
> a
2
, giving a well-known
quadratic quation for φ; the relation for
cutting it into three 0 < a
3
< a
2
< a
1
should satisfy
a
1
+a
2
+a
3
a
1
=
a
1
a
2
=
a
2
a
3
= φ
3
where φ
3
is the unique real root of a cu-
bic equation. This naturally generalizes
to φ
n
for all n. This leads to higher-
dimensional geometric analogues of the
golden rectangle, as well as to natu-
ral recursive generalizations of the Fi-
bonacci numbers.
