Abstract
This paper treats a special Hungarian tradition of mathematics and its teaching, which emerged at the end of the 19th century. First, I briefly explain the circumstances of the formation of high quality Hungarian mathematics in the late 19th- early 20th century, touching on the socio-economic and cultural context as well as the educational reforms of the period. In a second part, I focus on a specific group of first-rate Hungarian mathematicians and mathematics educators of the mid-20th century; all of them participated in discussions of educational questions during the 1940s, and later influenced the important mathematics educational reform of the 1960s and 1970s led by Tamás Varga. In the third part I analyse some of their writings (books popularising mathematics, papers about mathematics education, correspondences), in order to attempt to characterise their conception of the nature of mathematics and its teaching. The historical and the textual analysis will also show that some well-known thinkers of Hungarian origin like G. Pólya and I. Lakatos are in close relation to the tradition represented by this Hungarian group.
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- 1.
There exist mostly some commemorations on single mathematicians, by colleagues see e.g. the recent book about Rényi (2013). An interesting attempt, in English, to give a panorama on Hungarian mathematical life is that of (Hersh and John-Steiner 1993). A brief history of mathematics education can be found in Császár (2005) and in Frank (2012). About contemporary mathematics education, the comparative researches of Paul Andrews give some caracterisation (e.g. Andrews 2003; Andrews and Hatch 2001).
- 2.
The Hungarian mathematics education community remembers the reform led by Varga as a decisive moment which has significant influence on mathematics education until today: this is attested for example by the numerous commemorations on the yearly conference “Varga Tamás Napok” as well as by Szendrei (2007). For details on the reform movement in English, see (Halmos and Varga 1978).
- 3.
- 4.
E.g. in Varga (1975) he details who inspired him. Incidentally, these influences seem to arrive mostly from the western countries and less from the “Eastern bloc”. This phenomenon doesn’t seems to be unique for the case of Hungary: we plan to develop a research project with C. Radtka and S. Lawrence among others to study the ways of circulation between Eastern and Western Europe in the new math reform period.
- 5.
This work was the basis of a chapter of my thesis (Gosztonyi 2015a) where I compare the Hungarian reform led by Tamás Varga with the French “mathématiques modernes” reform of the same period, in order to understand the influence of the international discourses on one hand and the local traditions on the other hand on the characteristics of these reforms.
- 6.
It would be interesting to study the influence of this international reform movement, and more particularily of Felix Klein on the Hungarian mathematics education, as some interesting similarity can be found in their principles: e.g. the experimental nature of mathematics or the role attributed to intuition. (See e.g. Gispert and Schubring 2011).
- 7.
The Collegium gained its name after József Eötvös, the father of Loránd: lawyer, novelist and also Minister of Culture and Education, who was responsible for the 1868 law of education.
- 8.
KÖMAL is partly available in English; students may also participate in English in the competition by correspondence. See http://www.komal.hu/info/bemutatkozas.e.shtml for the English version.
- 9.
For details about Karácsony see (Kontra 1992).
- 10.
Kontra (1992) mentions the participation of Kalmár, Péter, Varga. About the participation of János Surányi, his son, László Surányi has given some information.
- 11.
In his recent article, Szabó attempts to demonstrate how the “social philosophy” of Karácsony and the role he dedicated to the pictures and visuality in his works influenced Kalmár’s thinking about mathematical research and mathematics education (Máté 2006; Gurka 2001; Szabó 2013). Karácsony appears several times in the correspondence of Kalmár and Péter, Kalmár and Varga: these references don’t give details about the nature of Karácsony’s influence, but confirm his importance for Kalmár and Varga.
- 12.
The mathematics research institute of the Hungarian Academy of Science today bears Rényi’s name: http://www.renyi.hu/.
- 13.
- 14.
See the preface of Playing with infinity (Péter 1961) where he appears as one of her most important references.
- 15.
These details are confirmed among others by Mária Halmos, one of his closest colleagues who was also a member of Surányi’s aforementioned team in Rényi’s research institute. See also (Máté 2006).
- 16.
For more detail about the role and appearance of the series of problems in the work of Rózsa Péter and Tamás Varga, see (Gosztonyi 2015b)—a paper published as part of the French “Series of problems” project in history of sciences (problemata.hypotheses.org).
- 17.
In this sense, the use of the Hungarian term seems to be similar to the German “Anschauung”.
- 18.
Probably that is what Lakatos meant when he called mathematics a ‘quasi-empirical science’. Lakatos invited Kalmár to take part in a conference on philosophy of mathematics in London in 1965, where he presented similar thoughts on the empirical nature of mathematics. Lakatos commented on his talk, which he later expanded in his article on mathematics as a quasi-emprical science (Kalmár 1967; Lakatos 1976b).
- 19.
Rényi himself refers to Szabó in the Postface of his Dialogues. (Rényi 1967, p. 91).
- 20.
About the relation of Szabó and Lakatos see (Máté 2006).
- 21.
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Acknowledgement
I am grateful for the financial support of the “Séries de problèmes, un genre au carrefour des cultures” research project (http://problemata.hypotheses.org/) developed in the framework of the HASTEC research program (http://www.labex-hesam.eu/fr/13-hastec-presentation). I would like to acknowledge the inspiring discussions to András Máté and Alain Bernard: they offered important help to develop this research. I am also grateful to Ernő Vincze, Mónika Fekete, Attila Pásztor and Esther Neumark for their help with the English language by writing my talks for the Mathematical Cultures conferences and the present paper.
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Gosztonyi, K. (2016). Mathematical Culture and Mathematics Education in Hungary in the XXth Century. In: Larvor, B. (eds) Mathematical Cultures. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-28582-5_5
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