48 Normat 61:1, 48 (2013)

Summary in English

Ulf Persson, Lars Hörmander

(Swedish)

A short obituary of a legendary Swedish

mathematician focusing on his early

rise.

Osmo Pekonen, Hur matematiken

bidrog till strukturalismens uppkomst

(Swedish).

Applications of mathematics are legio,

also in the social sciences, but in the

latter it is mostly in the form of stati-

stics. Thus it is somewhat remarkable

that also more abstract and conceptual

mathematics may enter in the so called

’softer sciences’ such as anthropology in

an honest way. The article discusses how

group theory can clarify the sophisti-

cated rules that govern intermarriage in

certain tribes. More speciﬁcally the non-

abelian group of order eight given by

the quaternions ±1, ±i, ±j, ±k plays a

crucial role. The central character is the

legendary anthropologist and mytholo-

gist Claude Lévi-Strauss who set up his

so called canonical formula, which was

given a mathematical interpretation by

his friend the Bourbakist André Weil.

R. Siegmund-Schultze, B. Øksen-

dal Johannes Lohne (1908-1993), den

glemte norske nyoppdager av Thomas

Harriot og frontkjemper for den tyske

okkupasjonsmakten under 2.verdenskrig

(Norwegian).

Thomas Harriot (1560-1621) was a bril-

liant British mathematician and phy-

sicist the true scope of whose achiev-

ments only became known much later

through the pioneering eﬀorts of the

Norwegian historian of science - Johan-

nes Lohne. The article does not only de-

scribe the work of Harriot but also more

signiﬁcantly explains how Lohne came

to discover and interpret them, which

was a highly non-trivial task. One phy-

sical example was the discovery of the

law of sine that characterizes refraction

and has traditionally been attributed to

Snellius and Descartes. A mathematical

example was the evaluation of what in

modern terms is given by

s

0

sec ◊d◊ and

of fundamental importance for the Mer-

cator projection. In the 16th century

there were no ready methods to attack

the problem, but the numerical values

Harriot was able to give were surprising-

ly accurate indicating a deep mathema-

tical understanding, further conﬁrmed

by his studies of stere ographic projec-

tion and logarithmic spirals in connec-

tion with the above projection. Added is

a biography of Lohne himself, not shy-

ing away from the less salutary aspects

of his life.

Hans Thunberg, Tonsättaren Per

Nørgårds "oändlighetsserie" (Swedish)

This article presents a mathematical de-

scription, in terms of recursively deﬁned

number sequences, of the algorithms de-

vised by the Danish composer Nørgård.

The ambition of the latter was to gene-

rate from a very short sequence of tones

melodies rich in symmetries and self-

similarities, melodies which could be

aperiodic and hence inﬁnite in length.

Given the mathematical presentation a

variety of results can be formulated and

proved. Note that the well-known Thue-

Morse sequence is essentially a special

case.