Abstract
Tatiana Afanassjewa (1876–1964) lived an era when women were not expected to study and often not permitted to enter academia. Yet, she managed to pursue her interests in mathematics and physics. After graduating from the Higher Women Courses in St Petersburg, where she specialized in mathematics and physics, she travelled to Göttingen to gain a deeper understanding of these fields. There, she also met her future husband, Paul Ehrenfest from Vienna, with whom she went on to build a life that was centered on the natural sciences. After some restless years in Vienna, Göttingen, and Saint-Petersburg, Ehrenfest became a professor in Leiden, but while his career thrived, Afanassjewa was confronted with many setbacks. This chapter sketches how she nevertheless, and next to raising four children and managing a busy household where learned guests from all over the world happily stayed over, succeeded to become an influential voice in the Dutch debates about the didactics of mathematics while also publishing original work in the field of thermodynamics.
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Notes
- 1.
The Dutch “Dispuut Gezelschap Christiaan Huygens” was established at the end of the nineteenth century and still exists today.
- 2.
Tatiana Afanassjewa herself always used this German transcription of her name when not in Russia, both privately and when publishing essays and research articles. It will be used in the current article as well.
- 3.
Hugo Ehrenfest to Paul Ehrenfest, 9 April 1924: Ehrenfest Archive, Museum Boerhaave Leiden (EA-MBL) 1.1.2.
- 4.
Ehrenfest himself inspired this notion, since he once compared Einstein to Holbein and Bohr to Rembrandt during a conversation with Robert Oppenheimer: Undated note from R. Oppenheimer to M. J. Klein, EA-MBL 12.1.
- 5.
Klein (1970).
- 6.
Marriage certificate, 21 December 1904: EA-MBL 2.2.
- 7.
Examples are thick walls that keep the house warm in winter and cool in summer; a heating system with horizontal pipes rather than radiators; double-glazed windows with large spaces between the inner and outer layers of glass; “lazy” stairs that are more likely to be found in Saint Petersburg than in Leiden. Sketches and building plans: Ehrenfest Family Archive (EFA).
- 8.
Einstein to Ehrenfest, 18 October 1916: The Collected Papers of Albert Einstein (CPAE) 8a, Doc. 268; Also cited in Klein (n.5) 304.
- 9.
The first detailed discussions of this work can be found in letters to Ehrenfest: CPAE 8a, Docs. 182, 185.
- 10.
See, e.g., CPAE 8a, Introduction.
- 11.
Einstein to Besso, 21 July 1916: CPEA 8a, Doc. 238.
- 12.
Senger and Ooms (2007).
- 13.
Biographical notes by son-in-law Henk van Bommel, undated: EFA.
- 14.
Mariç went to Zürich immediately after high school. See, e.g., Popović (2003).
- 15.
See, e.g., CPAE 9, Introduction.
- 16.
Einstein to Ehrenfest, 9 November 1919: CPAE 9, Doc. 155.
- 17.
Ehrenfest-Afanassjewa (1960). Personal details: from the preface to this collection of essays by Dutch mathematician Bruno Ernst [pseudonym of J.A.F. [Hans] de Rijk].
- 18.
Personal communication T. van Bommel.
- 19.
Hendrik Antoon Lorentz (1853–1928). For a concise biography, see Kox (2018).
- 20.
Lyubov Zapolskaya (1871–1943). Like Afanassjewa, she studied at the Pedagogical Institute, the Bestuzhev Institute, and then obtained her Ph.D. in Göttingen, with Hilbert (1901). In Russia, in Saratov, she then taught mathematics, among other subjects, and headed the department of Higher Mathematics and Mechanics at the Pedagogical Institute of Yaroslav. she-win.ru/nauka/588-lubov-zapolskaya.
- 21.
Nadezhda Gernet (1877–1943) first studied at the Bestuzhev Institute, and then obtained a Ph.D. with Hilbert in Göttingen (1902). She became a teacher at Bestuzhev, and went on to teach at the university, once its courses had merged with those at the Bestuzhev Institute. In 1930, she became a professor at the Polytechnic Institute in Petersburg: Editors A.N. Kolmogorov and A.P. Yushkevich, Mathematics of the 19th century (Basel 1998).
- 22.
Klein received support for his policy from the Prussian minister for education. E.g., Thiele (2011).
- 23.
Bonner (1995).
- 24.
Afanassjewa to M. J. Klein, undated: EA-MBL 12.1.
- 25.
Ehrenfest-Afanassjewa (n.17). Strikes and unrest in 1899 may have had a negative effect on the courses.
- 26.
The cities were different from the rural areas in Russia, where the majority of the population was illiterate.
- 27.
Koblitz (2013).
- 28.
www.prlib.ru/en/history/619592. Women could study History and Philology or Physics and Mathematics. After 1906, a third possibility was Law.
- 29.
Stites (1978).
- 30.
Currently the faculty of Earth Sciences of the University in Petersburg.
- 31.
Hans (1963). These words were not empty: As early as 1864 9,000 girls were enrolled in 29 girls’ schools of the first order (later called gymnasium) and 91 of the second order (later called progymnasium) and in 1869 another 32 girls’ schools had been established.
- 32.
Van Bommel (n.13).
- 33.
Sonya had sent Afanassjewa to a new private gymnasium, in a large building at the Ulitsa Kabinetskaya, slightly south of the Fontanka. The director, Maria Nikolyevna Stoyunina, applied the innovative pedagogical principles her husband, Vladimir Stoyunin, had described in lectures and books: teachers tried to foster individual talents, pupils were allowed to jump, run, and talk for 15 min between classes to refresh their minds, and they had gymnastics classes every day. Latin and Greek were not taught; the curriculum was a watered-down version of what boys were taught, according to what Afanassjewa said later [n. 17], “but the pedagogical methods were such as I would like to see them everywhere.”
- 34.
Called Pedagogical Courses of the Girls’ Gymnasium and, from 1903 on, Women’s Pedagogical Institute.
- 35.
Richard Stites (n.30); Morrissey (1998).
- 36.
Johanna Ehrenfest-Jellinek died 3 May 1892; Sigmund Ehrenfest died 10 November 1896.
- 37.
Van Bommel (n.13).
- 38.
In 1899, large-scale strikes and student protests took place, and they can be viewed as a prelude to the revolution of 1905, although in 1899 the students were still more preoccupied with academia and their own position than with society at large. Afanassjewa did not participate in these protests: she was among the women who believed in more gradual change and who were afraid that the Women’s courses would be closed in retaliation to protests. See Morrisey (n.34).
- 39.
Orest Chvolson (1852–1934) was a physics professor in Petersburg and was well known for his textbooks, which were translated into many languages.
- 40.
Shiff herself had completed her studies at the Women’s Courses in 1882. She had later obtained a Ph.D. in Göttingen and had become a teacher at the Women’s courses. She taught geometry and calculus, amongst other subjects, and published academic books and articles in Russian academic journals; she was one of the first Russian women who dedicated her life to mathematics: Mary (2015).
- 41.
Vera Shiff to Afanassjewa, 26 June/9 July 1901, EFA [translated from Russian to Dutch by Hans Driessen].
- 42.
Ehrenfest-Afanassjewa (n.17).
- 43.
Klein (n.5); Auditor-papers university Vienna: EA-MBL 2.4.
- 44.
Ludwig Boltzmann (1844–1906), who had been suffering from depression for many years, committed suicide during a vacation in Duino, Italy, in September 1906.
- 45.
Klein to Ehrenfest, 16 November 1906: EA-MBL 1.2.2.
- 46.
Later also referred to as the “flea model.”
- 47.
Paul had presented their “Urnmodel” at the Mathematische Gesellschaft at the beginning of November 1906. It later appeared as P. and T. Ehrenfest, “Über zwei bekannte Einwande gegen das Boltzmannsche H-Theorem,” Physikalische Zeitschrift 8 (1907) p. 311.
- 48.
P. and T. Ehrenfest, “Begriffliche Grundlagen der statistischen Auffassung in der Mechanik,” Encyklopädie der mathematischen Wissenschaften IV (Leipzig 1911). In English: The conceptual foundations of the statistical approach in mechanics (Ithaca 1959).
- 49.
Abram Ioffe (1880–1960) obtained his Ph.D. with Wilhelm Röntgen in Germany and then moved back to Petersburg where he would later, in Soviet times, become the director of the Leningrad Physico-Technical Institute (LPTI).
- 50.
Diary and notebooks: EA-MBL 1.2.6; Klein (n.5). Kruzhok means “small circle”: the papers were discussed within a small circle of physicists and mathematicians.
- 51.
- 52.
Ehrenfest spent some time in Leiden in the spring of 1903: notebooks 1903: EA-MBL 1.2.6; Klein, Ehrenfest (n.5).
- 53.
Frenkel (n.51).
- 54.
Koblitz (n.27).
- 55.
Maksheyev to Afanassjewa, 1 April 1908: EFA [translated from Russian to Dutch by Hans Driessen].
- 56.
Ehrenfest-Afanassjewa (n.17).
- 57.
Weigand et al. (2017).
- 58.
Ehrenfest-Afanassjewa (n.17) Chapter III.
- 59.
Undated handwritten manuscript of the questionnaire: EFA [translated from Russian to Dutch by Hans Driessen].
- 60.
Gustav Herglotz (1881–1953).
- 61.
Correspondence Ehrenfest and Afanassjewa, July and August 1910, EA-MBL 1.1.2; Diary, 23 July 1910 [translated from Russian to Dutch by Hans Driessen]; Pim Huijnen, Die Grenze des Pathologischen, het leven van fysicus Paul Ehrenfest, 1904–1912 (Master’s Thesis University of Groningen, 2003).
- 62.
- 63.
Frenkel (n.49).
- 64.
Ehrenfest had visited Leiden in 1903 (n.53) but the two men had not met each other since, and Lorentz was under the impression that Ehrenfest was a professor in St. Petersburg now (Klein, n.5).
- 65.
Ehrenfest & Ehrenfest (n. 48).
- 66.
Afanassjewa discussed a.o. a very preliminary report about the survey during the second All-Russian Congress for Mathematics Teachers in Moscow, early in 1914, but the project stagnated during the turmoil of the First World War, as she herself stated Ehrenfest-Afanassjewa (n.17).
- 67.
In Russia it was still December 1913.
- 68.
Ehrenfest to Afanassjewa, 9 January 1914, 11 pm: EA-MBL 1.1.1.
- 69.
Steen (2011).
- 70.
De Haan (1998).
- 71.
De Haas-Lorentz (1913); Original: Over de theorie van de Brown'schen beweging en daarmede verwante verschijnselen (Ph.D. Dissertation, University of Leiden 1912).
- 72.
A postcard from De Haas-Lorentz to Afanassjewa, 2 May 1956, also refers to “the many hours in which we discussed thermodynamics together and during which I learned so much from you”: EA-MBL 2.2.9:482.
- 73.
Hendrika van Leeuwen (1887–1974) coordinated the physics lab for students at the Technical University in Delft, carried out research into magnetism, and became the first female “lector” at this Technical University in 1947. See, e.g., Blaauboer et al. (2015).
- 74.
Personal communication A.J. Kox.
- 75.
Lorentz to Ehrenfest, 12 November 1912: EA-MBL: 1.2.2.
- 76.
Rommert Casimir (1877–1957) was also extraordinary professor of pedagogy at Leiden University between 1918 and 1947. At the Nederlandsch Lyceum, the first school of its kind, where, after two preparatory years, students could choose to focus on science (HBS) or opt for the curriculum of a traditional gymnasium.
- 77.
Ehrenfest-Afanassjewa (n.17).
- 78.
The first translated essay was “Over de rol der axioma’s en bewijzen in de meetkunde” in 1915: Ehrenfest-Afanassjewa (n.17).
- 79.
She published one more article in Russia in those years: Ehrenfest-Afanassjewa (1914).
- 80.
Theoretical physicist Hendrik Kramers (1894–952) worked with Bohr and later became professor in Utrecht, Leiden, and Delft; Physicist Jan Burgers (1895–1981) became professor in Delft and Maryland; Mathematician Dirk Struik (1894–2000) became professor at MIT; Physicist and meteorologist Dirk Coster (1889–1950) became professor in Groningen (he helped Lise Meitner escape from Nazi Germany); Samuel Goudsmit (1902–1987) was, among other things, head of the ALSOS mission of the Manhattan Project and worked in Brookhaven National Laboratory. Earlier, in Leiden, he had discovered electron spin together with George Uhlenbeck (1900–1988), who became professor in Ann Arbor and at the Rockefeller University in New York; Physicist and economist Jan Tinbergen (1903–994), who turned to economics at Ehrenfest’s instigation, was awarded a Nobel prize (1969); Theoretical physicist Hendrik Casimir (1909–2000) became director of the Philips Physics Laboratory (Natlab).
- 81.
- 82.
Family correspondence spring and summer 1922: EA-MBL 1.1.2.
- 83.
Alexander Friedmann (1888–1925) Russian mathematician and physicist.
- 84.
Ehrenfest to Afanassjewa, 1922: EA-MBL 1.1.2.
- 85.
Travel documents and correspondence, 1922: EA-MBL 2.2.9 and 2.2.2:435.
- 86.
T. Ehrenfest-Afanassjewa, http://www.math.ru.nl/werkgroepen/gmfw/bronnen/ehrenfest2.html (Den Haag 1924).
- 87.
Eduard Jan Dijksterhuis (1892–1965) was a Dutch mathematics teacher and author of several well-known books on the history of science with a focus on the role of mathematics: Klaas van Berkel (1996).
- 88.
- 89.
- 90.
- 91.
- 92.
Mandemakers (1996).
- 93.
- 94.
- 95.
Uffink (2001).
- 96.
Ehrenfest-Afanassjewa (1956); Correspondence with Brill: EA-MBL 2.2.9:428.
- 97.
Ehrenfest-Afanassjewa to Einstein, 18 August 1947: The Albert Einstein Archives at the Hebrew University of Jerusalem (AEA-HUJ), doc. 10–343.
- 98.
- 99.
Klein (n.5); Letters to relatives show that she mainly worked in Simferopol between 1926 and 1930 and in Moscow, where she stayed with the Mandelstam and Kagan families, from the end of 1931 until the middle of 1932; in Ordzhonikidze she worked from the end of 1932 until the middle of 1933: EFA [translated from Russian to Dutch by Hans Driessen].
- 100.
Ehrenfest-Afanassjewa in Moscow, to Ehrenfest in Leiden, 28 March 1932: EFA [translated from Russian to Dutch by Hans Driessen].
- 101.
Ehrenfest-Afanassjewa in Simferopol to C. Afanassjewa in Leiden, 24 March 1930: EFA [translation ibidem.].
- 102.
Afanassjewa to Galinka Ehrenfest, 12 July 1932: EFA [translation ibidem.].
- 103.
Trips of several months in 1923/1924 and in 1931/1932: family correspondence EA-MBL 1.1.2; Hollestelle (n.81).
- 104.
Ashwal (1990).
- 105.
Ehrenfest (1931); N.G. de Bruijn, In memoriam T. van Aardenne-Ehrenfest, 1905–1984, Nieuw Archief voor Wiskunde 3:4 (1985) 235–236.
- 106.
Family correspondence 1922–1933: EA-MBL 1.1.2.
- 107.
Afanassjewa-Maslova to Afanassjewa, 1931: EFA [translated from Russian to Dutch by Hans Driessen].
- 108.
Hollestelle (n.81).
- 109.
Hollestelle (n.81).
- 110.
Van Delft (2014).
- 111.
Correspondence Ehrenfest-Afanassjewa (1932): EFA.
- 112.
T. Ehrenfest-Afanassjewa (1931). The booklet contains exercises to increase the spatial awareness of students during a preparatory phase in geometry teaching.
- 113.
Afanassjewa to Ehrenfest, 15 August 1932: EFA [translated from Russian to Dutch by Hans Driessen].
- 114.
E.g., Pais (1991); Van Delft (n.110).
- 115.
E.g., Hollestelle (n.81).
- 116.
Personal communication T. van Bommel.
- 117.
- 118.
Pierre Auger (1899–1993) a French physicist who conducted cosmic ray experiments in which Pawlik was taking part.
- 119.
The man-made famine in Ukraine, 1932–1933, in which millions of Ukrainians died.
- 120.
In 1932, Ehrenfest’s former student Jan Burgers gave up his membership of the Dutch communist party, based on her advice. Personal communication Herman Burgers.
- 121.
Jacob Kloot (1916–1943) married Galinka Ehrenfest in 1941. Both wrote and illustrated children books under the name El Pintor, which were published by Kloot’s publishing house Corunda in Amsterdam. See, e.g., RKD Dutch Institute for Art History: rkd.nl/en/explore/artists/111285. In daily life, Jacob and other family members used “Kloots” as their family name.
- 122.
Galinka Ehrenfest was arrested while visiting new addresses to hide Jewish relatives and friends. She was released after one week in prison on 26 June 1943. Personal communication T. Van Bommel and documents from the German Sicherheitspolizei in EFA. After the war she married Henk van Bommel [n.13] and had a daughter with him.
- 123.
Afanassjewa requested to be allowed to teach the basic principles of mathematics and physics as a privaatdocent, associated with the University of Leiden in November 1940, shortly before the dismissal of Jewish professors and the famous protest speech of Prof. Dr. Cleveringa (26 November 1940). After this speech, the university was closed temporarily at first and, when the German authorities were unable to subject the university to Nazification, definitely in November 1942. Afanassjewa was granted the position on March 10 1941. She requested that the authorities terminate her contract on 11 May 1942. Her request was granted on 15 June 1942. The Secretary General of the Department of Education, Science, and Protection of Culture to Afanassjewa, 10 March 1941, accepting her as privaatdocent; Ibidem.15 June 1942, terminating her contract at her request: EA-MBL 2.5.
- 124.
Two sisters of Jaap Kloot stayed there temporarily: personal communication T. van Bommel. The elder brother of H. Langedijk stayed there at the end of the war, in order to escape the Arbeitseinsatz (forced labor and slavery in Nazi Germany) and during the week when H. Langedijk visited him, close to the end of the war, she counted at least four other people in hiding, among whom was the Jewish Mrs. Pinto: Personal communication. A certificate and letter testify that a tree was planted in Afanassjewa’s honor in the “Joop Westerweel-woud,” Ramat Menashe, Israel, by Mr. and Mrs. Schaap-Redak in 1946: EA-MBL, 2.2.32:453.
- 125.
Personal communication.
- 126.
Ehrenfest-Afanassjewa (1946).
- 127.
Although Tinbergen did not necessarily agree with all Afanassjewa’s views, he arranged for the work, which was published in 1946 at Boucher, The Hague, to be reviewed by the economist Prof. Dr. H.J. Seraphim in Weltwirtschaftliches Archiv: Tinbergen to Ehrenfest-Afanassjewa, 16 July 1955: EA-MBL 2.2.9: 482.
- 128.
Schrödinger to Burgers, 22 March 1946: EA-MBL 2.2.9:482. In the following years, Schrödinger would summarize his ideas in Schrödinger (1952).
- 129.
Afanassjewa to Einstein, 17 August 1947: (AEA-HUJ), doc. 10–312.
- 130.
Dukas to Afanassjewa, 17 April 1946: EA-MBL 2.2.1: 418; Prue Smedts to Afanassjewa, 30 September 1945: EA-MBL 2.2.1:418.
- 131.
The parcels were prepared by Mimosa Food Parcels in New York: EA-MBL 2.1.
- 132.
Einstein to Afanassjewa, 28 March 1947: EA-MBL 2.1. Einstein comments on her request.
- 133.
Afanassjewa to Einstein, 17 August 1947 (n.129).
- 134.
Einstein to Afanassjewa, 12 August 1947: EA-MBL 2.2.9: 482.
- 135.
See also (n.97): “I believe my book relates to an introductory—and more experimentally oriented—course (in thermodynamics), as Euclid’s Elements (no arrogance) relates to an introductory geometry.”
- 136.
Einstein to Afanassjewa (n.134).
- 137.
Ibid.
- 138.
Afanassjewa to Einstein (n.97).
- 139.
Einstein to Ehrenfest, 9 November 1919: CPAE 9, Doc. 155. Also cited in Klein (n.5) 313.
- 140.
Afanassjewa to Einstein, 28 December 1948: (AEA-HUJ) Doc.10–314.
- 141.
Einstein to Afanassjewa, 18 April 1953: EA-MBL 2.1.
- 142.
Lecture notes of her course on thermodynamics 1947/1948 are available in the Gorlaeus Library, Leiden University.
- 143.
De Moor (1999).
- 144.
Hans Freudenthal (1905–1990) was a professor of mathematics at Utrecht University, who later specialized in the didactics of mathematics. The Freudenthal Institute for Science and Mathematics Education at Utrecht University is named after him. See also, e.g., Bastide-van Gemert (2006); Molenaar (1994).
- 145.
De Moor (1993).
- 146.
Correspondence: EA-MBL: 2.2.9:482.
- 147.
Paul and Tatiana Ehrenfest (1959).
- 148.
Klein (n.5) 121.
- 149.
Ehrenfest & Ehrenfest (n.147) 7–9.
- 150.
- 151.
Ehrenfest-Afanassjewa (n.17).
- 152.
Private communication.
- 153.
Afanassjewa died at her home in Leiden on 14 April 1964.
- 154.
Van Hiele G. Krooshof (1964a).
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Acknowledgements
I would like to particularly thank Dr. Henriette Schatz for carefully correcting mistakes in the text and for her helpful suggestions; Prof. Dr. Jos Uffink for extremely valuable discussions about, among other things, Afanassjewa and thermodynamics; Prof. Dr. Anne Kox for pleasant and encouraging conversations throughout the project, Prof. Dr. Diana Kormos-Buchwald for her help in locating letters from Afanassjewa to Einstein, the late Dr. Ed de Moor for helpful conversations about Afanassjewa and the didactics of mathematics, Tamara van Bommel for opening up the family archive and Dr. Hans Driessen for carefully translating the many Russian texts. Finally, I would like to thank Stichting Physica for a grant (2,200 euros) for translating these Russian texts.
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van der Heijden, M. (2021). Tatiana Ehrenfest-Afanassjewa: No Talent for Subservience. In: Uffink, J., Valente, G., Werndl, C., Zuchowski, L. (eds) The Legacy of Tatjana Afanassjewa. Women in the History of Philosophy and Sciences, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-030-47971-8_1
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