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MATHEMATICS.
481
ingenious physicist of versatile endowments, famous chiefly for his discoveries in
optics, was an eminent mathematician for his time, without, however, having
achieved any work that can be regarded as forming a link in the general
development of mathematics. As a teacher he enjoyed a high reputation, and he
raised the mathematical instruction at Uppsala to a standard that kept pace with
the scientific claims of the time.
K. J. D. Hill (1793/1875) was a gifted mathematician and produced a large
number of works on the subject. E. G. Björling (1808/72) and K. F.
Lindman (1816/1901) were noteworthy investigators within the higher analysis and
are especially meritorious as authors of text-books on elementary mathematics.
K. J. Malmsten (1814/86) is epoch-making for mathematical studies in
Sweden and has asserted his position in the history of mathematical science,
principally on the strength of his work on the Euler summation formula. Malmsten,
in his capacity of professor at Uppsala (1842/59), managed in a short space of
time to raise the standard of mathematical instruction to a level with the
universal scientific standpoint of the time. Hj. Holmgren (1822/85) attracted
attention by his researches about the differential calculus with fractional indices;
he also possessed an eminent talent as a teacher and lecturer. The same may
be said of F. V. Hultman (1829/79), who, like Björling, deserved exceedingly
well of the elementary instruction in Sweden. K. E. Lundström (1840/69)
treated with great acumen certain problems in the calculus of variations.
During the last decades, Swedish mathematicians have been partaking in the
work for the development of mathematical science in a way that has attracted
great attention. This may be maintained concerning the two State universities as
well as the newly established Private University of Stockholm.
The present advocates for mathematics at the State universities are
M. Falk at Uppsala (born 1841) and C. F. E. Björling at Lund (born 1839),
the former of whom has treated various questions of algebraic analysis and the
theories of differential equations and of functions, whereas the latter preponderantly
has been devoting his work to geometry. Amongst other mathematicians who have
developed any considerable activity as authors may be mentioned: for Uppsala
H. T. Daug (1828/88; infinitesimal goometry), G. Dillner (born 1832; theory
of functions, differential equations), and A. Berger (1844/1901; theory of numbers).
At the university of Lund A. V. Båcklund (born 1845) has achieved important
researches, both within the domain of geometry and that of the theory of partial
differential equations; T. Brodén (born 1857) and A. Wiman (born 1865), now
at the University of Uppsala, have also been occupying themselves with
geometrical questions; besides those, Brodén has written several papers on the theory
of functions and Wiman on certain parts of the higher algebra.
Through the foundation of the Private University of Stockholm (1878)
— where, at the instruction, stated examination claims have not necessarily been
to take into consideration and where thus scientific investigation is working under
specially favourable circumstances — and by the starting (1882) of an international
mathematical Review, the Acta Mathematica, under the editorship of G.
Mittag-Leffler — Swedish mathematics has made considerable progress. This periodical,
which among its collaborators counts many of the most prominent mathematicians
of the time, occupies a position of note in the mathematical work of investigation
in our days — a circumstance which is a good testimony of the corresponding
development of the mathematical science in Sweden itself.
The first teachers of the subject in question at the University of Stockholm
were G. Mittag-Leffler (born 1846) and Sonja Kovalevski (1850/91).
Mittag-Leffler’s chief works are the treatment of the problem of analytically setting forth
functions of one variable in such a form as to reflect the characteristic attributes
of the functions without the introduction of extraneous elements, also the con-
Sweden. 31
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