96 Normat 56:2, 96 (2008)

Summary in English

Nils Baas and Christian Skau, Sel-

bergintervjuet II- Såldmetoden, Prim-

tallsatsen og Erdös (Norwegian).

This is part two of four of an interview

with Atle Selberg. It is mainly mathe-

matical. It takes up the story after his

completion of his doctorate and how he

through the methods of sieves was ab-

le to get an elementary proof (i.e. not

using complex analysis) of the prime

number theorem. A few years later he

was awarded the Fields medal, partly

because of this. However, partial results

of his leaked out, and Paul Erdös pick-

ed up on them, and saw how they could

be exploited for that purpose. His int-

erference greatly irritated Selberg, who

tried to throw him oﬀ the scent by tel-

ling him that it did not work. This back-

ﬁred as it only provoked Erdös, who was

able to prove a crucial formula, and led

him to believe that he had succeeded

where Selberg had failed. Erdös then

considered the proof of the Prime Num-

ber Theorem (including the basis provi-

ded by Selberg) to be joint work, which

Selberg refused and was later able to

provide an elementary proof also wit-

hout Erdös result. The controversy has

been a painful subject to Selberg and

he has deliberately suppressed it. But at

the interview he displayed a conﬁdenti-

al referee report on the matter written

by H. Weyl to N. Jacobson and which

was given to him as Weyl left the In-

stitute. In that report Weyl corrobora-

tes Selberg by presenting his view that

the achievement was fully due to Sel-

berg himself.

R. Høibakk, T. Jorstad,

D.Lukkasen and P. Lystad, Integer

crossed ladders; parametric representa-

tions and minimal integer values. (Eng-

lish).

Two crossed ladders of given length are

leaning against two opposite vertical

walls at a given height. Determine the

distance between the walls, and where

the ladders touch the walls, with parti-

cular emphasis on integral solutions.

Frank Bengtson, Om Bingospil (Da-

nish).

This explores various combinatorial as

well as probabilistic aspects of the game

Bingo, in which random ’tablets’ with

numbers arranged rectangularly are to

be matched with a given sequence being

called out.

Hans Georg Killingbergtræ, Paral-

lel axial Helixes in the double winding

surface (Norwegian).

In addition to the usual family of coaxi-

al helixes on a winding surface cut out

by concentric cylinders there are also

excentric ones cut out by cylinders con-

taining the axis. Those are naturally

appearing as contours of the shadow for-

med by light falling on the surface.