188 Normat 53:4, 188 (2005)

Summary in English

Helge Holden, Peter D. Lax. Abel

prize winner 2005 (Norwegian).

The author describes the work of this

year’s Abel Laureate, Peter D. Lax,

from the Courant Institute of Mathe-

matical Sciences, New York University.

Lax has given deep and penetrating con-

tributions to several areas of mathemat-

ical analysis, both pure and applied.

The focus of this article is on his con-

tributions to the theory of hyperbolic

conservation laws and to the theory of

soliton equations.

Regarding conservation laws, Lax

proved the ﬁrst general existence the-

orem for a system of conservation laws

with Riemann initial data, and he intro-

duced important numerical methods for

these equations. His seminal results are

a vital ingredient of all subsequent work

in the area.

In the theory of solitons, Lax in-

troduced what is now called the Lax

pair for the Korteweg–de Vries equa-

tion, an equation that describes a class

of surface waves on water. This was the

starting point for an incredible develop-

ment for all types of soliton equations,

such as the Boussinesq equation, the

Kadomtsev–Petviashvili equation, and

the sine-Gordon equation.

A modiﬁed version of the article in

English can be found at the web site

www.abelprisen.no, where one also can

ﬁnd computer simulations of some of the

results described in this article. In ad-

dition one can ﬁnd an interview with

Peter Lax. A Spanish translation of

a modiﬁed version appeared in Boletin

del departemento de matemáticas, Uni-

versidad Nacional Autonoma de Mexico,

no. 167–8, 2005, and Matematicalia, see

www.matematicalia.net.

Ülo Lumiste, Helmut Piirimäe,

Sven Dimberg, an introductor of New-

ton’s Principia into the University of

Tartu in the 1690s, part 1. Translation

by Jaak Peetre and Staﬀan Rodhe with

annotations (Swedish).

This is the ﬁrst part of three dealing

with Sven Dimberg, a Swedish profes-

sor of mathematics in Tartu, Estonia,

in the 1690s. He is supposed to have in-

troduced Newton’s Principia in the cur-

ricula of the university.

The article has set its aim as 1) de-

scribing Sven Dimberg’s life and work

on the basis of possibly ample source

material, and 2) trying to clarify when

and to what extent Newton’s theory was

really taught at the university.

The ﬁrst part tells about Dimberg’s

studies in Uppsala with Professor Bill-

berg as a supervisor, his travel abroad

and his stay in Turku, Finland, as a

university lecturer. He was in Turku for

one year in 1689/1690, during which he

presided for just one gradual examina-

tion. The thesis, certainly written by

Dimberg himself, was a mathematical

discussion of loan and interest. Here

sums of sequences and series are treated

for the ﬁrst time in Turku.

The annotations by the translators

provide new material for understand-

ing the possibility that Dimberg was

a pioneer of teaching Newton’s Prin-

cipia. They also give new information

about Dimberg’s biography and discuss

his benefactors, among them members

of the noble families De la Gardie, Ox-

enstierna and Gyllengrip.

Giorgio T. Bagni, Mathematics edu-

cation and historical references: Guido

Grandi’s inﬁnite series (English).