Norsk matematisk tidsskrift Norwegian mathematical journal 1919 1952

Norsk matematisk tidsskrift (Norwegian mathematical journal, 1919 -1952): a semi-popular organ of the Norwegian Mathematical Society Circulating Mathematics via Journals: The Rise of Internationalisation 18501920 Conference at the Mittag-Leffler Institute, June 2016 Reinhard Siegmund-Schultze University of Agder, Norway

Abstract: Norsk matematisk tidsskrift (NMT) was founded in 1919, in the aftermath of the foundation of the Norwegian Mathematical Society (NMSD, 1918). The journal was financed partly by the Norwegian state, by the Nansen Fund, and by insurance companies. The main founder was immigrant from Denmark, Poul Heegaard, who had experience from the editing the older Danish Matematisk Tidsskrift. Even though original plans to publish doctoral theses of young Norwegians in NMT were abandoned after founding a special series for this purpose, NMT’s role was not restricted to communication between various members of the NMS, among them teachers, researchers and students. It also carried valuable survey articles, e. g. on number theory, numerical analysis and on historical topics, the latter often connected to Abel and Lie. In 1952 the publication of NMT was discontinued in favour of two joint Scandinavian (Nordic) journals, one semi-popular and published in Scandinavian languages, called Nordisk Matematisk Tidskrift (NORMAT), one research oriented and published in English, called Mathematica Scandinavica. Both journals were primarily destined to contain contributions from Scandinavian mathematicians. At that time Acta Mathematica had reached such a broad international standing that its unofficial Scandinavian subtitle Nordisk Matematisk Tids(s)krift was dropped.

Scandinavian Mathematical Journals, in addition to Acta Mathematica Denmark: Mathematisk tidsskrift (1859 -1871, Schjellerup, Tychsen) Tidsskrift for mathematik (1871 -1888) – Zeuthen (DMF founded 1873) Nyt tidsskrift for matematik (1890 -1918), serie A: popular, ser. B: scientific (Dansk) Matematisk Tidsskrift (1919 -1952) Norway: Archiv for Mathematik og Naturvidenskab (1876 -1961) - Norway Norsk Matematisk Tidsskrift (1919 -1952) Norsk matematisk forenings skrifter (1921 -? ) Joint Scandinavian enterprises (note: Swedish Math. Soc. founded only 1950) Mathematica Scandinavica (1953 -) – scientific, English language Nordisk Matematisk Tidskrift (NORMAT)1953 – popular, Scandinavian languages Specialized journals: Skandinavisk Aktuarietidsskrift (1919 -1973) Scandinavian Actuarial Journal (1973 -)

Published many important articles by Lie. When state support was in danger in 1916, Ludvig Sylow (1832 -1918) wrote in a memo that the journal was the only outlet where unlike the Academy Proceedings - nobody else had to take responsibility or had to invest much work into the publication: “The young mathematician needs a journal where he can publish his work on his own responsibility but which has at the same time reputation both at home and abroad. ” [„Den begyndende Mathematiker behøver netop et Tidsskrift, hvor han kan faa sit Arbeid trykt påå eget Ansvar og netop et Tidsskrift af Anseelse ude og hjemme”. ]

Foundation of Norsk Matematisk Forening and of its journal N. M. Tidsskrift, according to Thalberg (1943 in NMT) Quotes from the protocol on the foundation of Norwegian Mathematical Society (Norsk Matematisk Forening, NMF) by actuary Arnfinn Palmstrøm (1863 -1922): “ 27 September 1918 the following gentlemen: Professor Alf Guldberg – professor Poul Heegaard – professor Carl Størmer – docent Th. Skolem – rektor Magnus Alfsen – overlærer (senior teacher) Anton Alexander – overlærer Anders Søgaard – actuary Dr G. Holtsmark – actuary N. Solberg – cand. real Viggo Brun – stud. real Trygve Nagel – actuary A. Palmstrøm met in the (Kristiania-Oslo) office of the last mentioned at the Brage Life insurance Company in order to discuss the foundation of a Norwegian mathematical society and, in connection, the publication of a mathematical journal. The committee sent applications for economic support to life insurance companies and banks through Den Norske Bankforening + an application for state support to the Church- and Education Ministry. “ Carl Størmer was elected “foreman” of the new NMF, which was founded 2. November 1918, again organized by Palmstrøm from the insurance company. The latter remarked on the meeting that foundation would not have come about without the move by Danish born Poul Heegaard to Norway in 1918: “He had many years experience as editor of a mathematical journal in Copenhagen”

The table of contents at the right is from 8 (1926)

Examples for mathematical survey articles in NMT (as a rule in Norwegian) Størmer, Carl: A numerical method for the integration of differential equations (1921) Nagel, Trygve: Fermat’s problem: a survey article (1921) Birkeland, Richard: Relativity theory and classical mechanics (1923) Næss, Almar: Short introduction into vector analysis (1923/24) Ore, Øystein: Algebraic and transcendental numbers (1924) Skolem, Thoralf: Survey of the most important discussions on the foundations of mathematics (1926) Skolem, Thoralf: On mathematical logic (German, 1928) Johansson, Ingebrigt: Non-Euclidean Geometry from projective standpoint (1930) Brun, Viggo: The Gauss distribution (1932) Lorey, Wilhelm: The mathematician and numerical analysis (German, 1933) Rosseland, Svein: On the differential analyzer (1937) Dehn, Max: On Ornaments (German 1939) Harkin, Duncan: The Development of Modern Algebra (English 1951)

Carl Størmer (1874 -1957) Øystein Ore (1899 -1968)

Examples for mathematical research articles in NMT (as a rule in Norwegian) Nagel, Trygve: On higher congruences with primepower modulus (German, 1919) Nagell, Trygve: On the indeterminate equation x 2 – D y 2 = 1 (1925) Ålander, Martin: On a property of a meromorphic function (German, 1926) Beurling, Arne: Generalisation of an inequality by Cauchy (French, 1932) Popgen, J. : On the irrationality of the tangens of a rational number (Dutch, 1944) Selberg, Atle: Remarks on a multiple integral (1944) Götlind, Erik: A system of axioms for the propositional calculus (1947)

“Already during its first year in 1919 NMT received many more manuscripts than it could print due to lack of space. The pressing economy restricted the number of pages. However, due to support by well-to-do men and specially after Heegaard’s appeal “Videant Consules” in volume 1920 (p. 48) the printing of mathematical papers outside the NMT was organized as “Norsk Matematisk Forenings skrifter” (since 1921 and in single issues). ” (Thalberg, NMT 1943) Topologist Poul Heegaard (1920): “The situation has now become such that one has to wait several years before one can hope that a scientific work will be published, … which can change scientific employment into a luxury for rich people with a taste for it. … The efficiency of money spent on publishing has been reduced to one fourth. ” Poul Heegaard (1871, Copenhagen – 1948, Oslo)

Norsk matematisk forenings skrifter (selection) Richard Birkeland (1879 -1928): “Om opløsning av algebraiske ligninger ved en sum av hypergeometriske funktioner av en eller flere variable, ” ser. 1, no. 1 (1921) Alf Guldberg (1866 -1936): “On correlation, ” ser. 1, no. 5 (1921) Almar Næss (1888 -1965): “Zur Theorie der Triaden im dreidimensionalen Raum, ” ser. 1, no. 6 (1921) Øystein Ore (1899 -1968): “Über höhere Kongruenzen, ” ser. 1, no. 7 (1922) Trygve Nagel (1895 -1988): “Über die Reduktabilität in algebraischen Zahlkörpern, ” ser. 1, no. 9 (1922) Trygve Nagel: “Résultats nouveaux de l'analyse indéterminée : 1, ” ser. 1, no. 8 (1922) Ragnar Frisch (1895 -1973): “Sur un problème d’ économie pure, ” ser. 1, no. 16 (1926)

This is the table of content for volume 31 (1949) The order with main articles, smaller communication, internal problems of the Society and assignments of highschool pupils is kept. However, now, during and after the war, the percentage of research articles has increased as the contributions in the middle of the table show.

Examples for historical and pedagogical articles in NMT (as a rule in Norwegian) Brun, Viggo: On the mathematics of the Indians (1919) Skolem, Thoralf: Ludvig Sylow and his scientific work (1919) Størmer, Carl: On the mathematical seminar founded by Elling Holst in 1886 (1919) Heegaard, Poul: On the main traits of H. G. Zeuthen’s scientific work (1920) Sylow, Ludvig: Evariste Galois (1920) Alfsen, Magnus: Infinitesmal calculus at high schools (gymnas) (1921) Engel, Friedrich: Sophus Lie and his collected works (1922) Bjerknes, V. , Brun, V. , Olsen, E. , Lange-Nielsen, Fr. : Axel Thue (four separate articles, 1922) Thalberg, Olaf: Mathematics and poetry (1923) Zeuthen, H. G. : On the first decades of the London Mathematical Society (1925) Thalberg, Olaf: Recreational mathematics at school (1926) Lange-Nielsen, Fr. : On the history of Abel’s theorem (German, 1927)

More examples for historical and pedagogical articles in NMT Piene, Kay: Abstract mathematics, reality mathematics and school mathematics (1928) Arvesen, Ole Peder: On the foundation of descriptive geometry with Monge (1928) Special issue 1929 on the occasion of the centenary of Abel’s death Heegaard, Poul: A glimpse of old Egyptian mathematics (1931) Størmer, Carl: The Indian Ramanujan – a remarkable mathematical genius (1934) Piene Kay: The position of mathematics at the Norwegian higher schools after 1800 (1937/38) Brun, Viggo: On the squaring of the circle (1941) Thalberg, Olaf: The Norwegian Mathematical Society through 25 years (1943) Brun, Viggo: Abel’s lost manuscript (1949) Brun, Viggo: The presentation of mathematics during history (1950)

Example of a book review by V. Brun (NMT 1939), critical of Bieberbach’s racist theories In his 1939 book “Irrational numbers” Perron alluded to Bieberbach’s review of the first edition (1920) where B. preferred the Cantor–Méray theory of real numbers. Perron in 1939 ‘defended’ his own preference for the undoubtedly ‘German’ Dedekind, who happened to be the true spiritual mentor to the ‘Jewish’ algebraist Emmy Noether, with the following words: “A warning from such competent side must not be ignored without serious reasons, the more so since its importance has recently much increased due to the well-known research on the J- and Stype of mathematicians. [However …] I believe a German who has the choice between a German product and an equally beautiful and valuable product of foreign origin should be allowed to follow his heart and to prefer the German one because it is German. ” (Perron 1939, vi)

“During the Kant-Coppernicus week in 1939 the German mathematician Kähler said in a talk: ‘Those who have immersed in the mathematics from the century when Kant and Euler lived are overwhelmed by a longing for old mathematics such as many people have a longing for old music. ’ Is this perhaps because the old mathematicians had more time then we have? The so-called telegram style has unfortunately spread over the entire mathematical literature. The exponent for this style is the otherwise very meritorious mathematician Landau, who was professor in Göttingen until 1933. …I do not think we should let ‘die straffe Gliederung’ [German for concise and short presentation] become the ideal for mathematical presentation. ” Here Brun shows no political correctness at all after the war: applauding the Nazi Kähler during a nationalistic event. Ignoring the Jewish mathematician’s Landau’s dismissal 1933 in Göttingen! Norwegian mathematics in its distance from the continent both in positive and negative respects!

The reorganization of Scandinavian Mathematical Journals in 1953

From the preface of volume I (1953) of NORMAT Elementary mathematics – including problems of teaching – has had for a longer period broad possibilities of publication in nordic countries. It has found space in the Danish Matematisk Tidsskrift (founded 1859, from 1890 divided in an elementary series A and an advanced series B), in Norsk Matematisk Tidsskrift (from 1919) and in two Finnish journals Matemaattisten Aineiden Aikakauskirja (from 1936) and Arkhimedes (from 1949). But none of these publications had pan-nordic ambitions and although they have been known outside their own countries, they were more oriented towards the latter. A collective organ for elementary mathematics has not existed in the North. … The new journal hopes to provide connections between research and teaching, create personal contacts between those interested in mathematics and counteract isolation and stagnation.

INFOMAT April 2013: warning against imminent “burial” of NORMAT “An appeal for NORMAT” The Swede Persson refers to the tradition of NMT and the NMF, which was founded “more than 30 years before its Swedish counterpart”. He mentions problems of popularization in mathematics, competition by Bulletin AMS, lack of economic support. Thus in 2013 not even one issue for 2012 had appeared.