Normat 54:1, 47–48 (2006) 47

Summary in English

Henrik Kragh Sørensen, The Scan-

dinavian Congresses of Mathematics

until the end of World War I. (Dan-

ish).

The modernisation of science and so-

ciety around the turn of the twentieth

century meant increasing specialisation

in mathematics and new importance

attached to international contacts. In

Scandinavia, from where mathemati-

cians had traditionally oriented them-

selves towards the mathematical centres

in Germany and France, an idea of in-

creased independent, regional coopera-

tion soon caught on. This was the vi-

sion of one very important and energetic

Swedish mathematician, in particular;

namely Gösta Mittag-Leﬄer.

The Scandinavian countries shared a

common linguistic and cultural back-

ground to such an extent that acad-

emic exchange and coop eration would

be eased by it. Furthermore, they shared

the role of “small nations” in an increas-

ingly imperialistic world order. That

role, as small and most often neutral na-

tions, gave the Scandinavians the possi-

bility to mediate in regional and global

conﬂicts. After the dissolution of the

Union between Sweden and Norway

in 1905, the ﬁrst Scandinavian (later

properly renamed “Nordic”) congress

of mathematics served as an extended

hand aimed at healing the wounds and

furthering professional cooperation.

Although nobody doubted the uni-

versal nature of mathematics, the Scan-

dinavian meetings b ec ame a welc ome

regional opportunity for professional

and more congenial exchanges. Four

such meetings were held before the end

of World War I; these meetings are

analysed and discusse d in the present

paper. This ﬁrst part of the paper cov-

ers the congresses in 1909 and 1911; the

subsequent two will be covered in a sec-

ond part. In many ways, the story comes

full circle when the narrative reaches

1916: By then, Scandinavian mathe-

maticians had proved their worth to the

international world of mathematics, and

the role of the small nations in world

politics after the war was yet to be de-

ﬁned.

The Scandinavian congresses of

mathematics constitute an integrated

part of the complex process of profes-

sionalisation of mathematics whereby

an identity as “a mathematician” was

being negotiated. Many of the discus-

sions – be it the political ones or the

identity-forming ones – took place in

the Scandinavian newspapers and these

newspapers have been extensively used.

They also provide an interesting per-

spective on the image of mathematics

as presented in the media.

Ülo Lumiste, Helmut Piirimäe,

Sven Dimberg, an introductor of New-

ton’s Principia into the University of

Tartu in the 1690s, part 2. Tran slation

by J. Peetre and S. Rodhe (Swedish.)

This is the second part of three deal-

ing with Sven Dimberg, a Swedish pro-

fessor 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.

Dimbe rg’s activity at Tartu Univer-

sity is considered, including his teach-

ing, which mostly involved Newton’s

48 Summary in English Normat 1/2006

Principia. There is also a discussion of

the theses supervised by him. On his

own expense he bought “mathematical

instruments” for the university, as the

greedy King Charles XI did not provide

any funds for this purpose. In 1697 he

took a leave of absence and went to

Stockholm, his apparent purpose being

to apply for several professorships at

Uppsala. This leave was prolonged sev-

eral times, and Dimb erg never returned

to Tartu. In 1699 the university was

moved to the seaport Pärnu. Dimberg

got the assignment to design an astro-

nomical observatory on the roof of the

new university building there. The year

after, the devastating Great Northern

War broke out, eventually annihilating

a great part of the population of the

Province of Livonia (present day Es-

tonia and Latvia). Dimberg’s leave of

absence was prolonged several times,

but ﬁnally the new King Charles XII

get fed up with him, and, in 1701, he

was dismissed along with some other

disobedient professors. This put and

end to Dimbe rg’s academ ic career. Once

more, in 1703, he tried to apply for a

job in Uppsala, but to no avail. The

rest of his life Dimberg served as ju-

rist in the service of several law courts

ﬁrst in Riga (1706-1709); the city fell to

the Russ ians the year after, and then in

Finland (Turku) and, ﬁnally, in Sweden.

In 1719, Dimberg was raised to nobility,

and he assumed the name Dimborg. In

1731 he died, childless, so his line died

out with him.

Audun Holme, Some glimpses from

the history of mathematics: The contro-

versy between Newton and Leibniz, and

a little more. (Norwegian).

The author gives a brief account

of Newton’s childhood and education,

his early career and appointment to

the Lucasian Chair at Cambridge, suc-

ceeding Barrow. Wallis, whose work

inspired Newton very much, was en-

gaged in a bitter debate with the im-

portant philosopher Hobbes, ostensibly

over geometry but probably in reality

over free thinking atheism versus pious

Christian faith.

The great and tragic controversy

was, however, the one between Ne wton

and Leibniz. Newton felt convinced that

Leibniz had plagiarized his great work,

which constitutes the foundation for our

present day mathematical analysis and

calculus. But no scientist works in a vac-

uum, and these ideas were, arguably, so

to say in the air at the time of New-

ton and Leibniz. The author brieﬂy in-

dicates the diﬀerence between Newton’s

and Leibniz’ approaches.

Newtons theory was diﬃcult to

grasp, while Leibniz had a more sugges-

tive notation and was more easily ac-

cessible. The diﬃculty in Newton’s the-

ory met with scorching criticism from

Berkeley, and Hooke was no friend og

Newton’s. Halley, however, supported

Newton and his work in ways which

were quite decisive.

In continental Europe the mathe-

maticians, siding with Leibniz, lost no

time in availing themselves of the the-

ory and notation develope d by him.

Among them the mathematical fam-

ily Bernoulli were particularly impor-

tant. Johann Bernoulli p ose d the fa-

mous problem of the baristochrome, in

his journal Acta Eruditorum. The prob-

lem was sent to Newton, now warden of

the Royal Mint. Some say this was done

to embarrass him, but Newton immedi-

ately solved the problem.

The author concludes w ith a short

account of Niels Henrik Abel’s work, as

a young boy, with a vastly more general

problem, anticipating the modern the-

ory of integral equations.