EHRENFEST-AFANAS’EVA, TATIANA A.

(also Afanasyeva, Afanassjewa, Tatyana, Tatjana, b. T. Alekseevna Afanas’eva, m. Ehrenfest) (b. Kiev, in Ukraine, Russian Empire 19 November 1876;

d. Leiden, The Netherlands 14 April 1964), mathematics, statistical mechanics, mathematics education.

Tatiana Ehrenfest-Afanas’eva was a Russian-Dutch mathematician. She was married to the Austrian physicist and mathematician Paul Ehrenfest (1880–1933). Tatiana and Paul Ehrenfest were a couple in science; they collaborated closely together, especially on their classical review of the statistical mechanics (1911) of Ludwig Boltzmann (1844–1906). She published articles on different topics, including randomness (1956), entropy (1958), and methodological problems concerning how to teach children in mathematics and geometry (1931). She also collaborated with the German-Dutch mathematician and historian of mathematics Hans Freudenthal (1905–1990) and the Dutch historian of science Eduard Jan Dijksterhuis (1892–1965).

Tatiana and Paul Ehrenfest had two daughters and two sons: The oldest daughter, Tatiana (Tanja) P. Ehrenfest, married Tanja van Aardenne-Ehrenfest (1905–1984), and became a mathematician too; Galja (also Anna), married A. van Bommel-Ehrenfest (1910–1979), and became an author and illustrator of children’s books; Paul Jr. (1915–1939) studied physics. The youngest son Vassily (1918–1933) had been born with Down syndrome. In 1933 Paul Ehrenfest, suffering from depression, shot Vassily and then killed himself.

Early Years . Tatiana Alekseevna Afanas’eva was born in Kiev in the Ukraine, which at the time belonged to the Russian Empire. Little is known about her parents and her childhood. After the death of her father she lived with an uncle in St. Petersburg. She received a good education at a girl’s school in St. Petersburg and attended a women’s pedagogical school. Becoming a teacher was an acceptable profession for a young woman in that period. Furthermore, she could attend the Women’s College in St. Petersburg where young women could obtain relatively good scientific training. As was the case with many women from Russia, Tatiana Afanas’eva went to Germany after graduating from school and became one of several Russian women students at the University of Goettingen. She studied mathematics and in 1902 met Paul Ehrenfest, who received his doctoral degree in 1904. They wed the same year.

The couple lived in Germany and Austria, but because of the then-normal anti-Semitism at German and Austrian universities, it was difficult for him, a Jew, to get an academic position. His marriage to a Russian woman, a foreigner, made the situation even more complicated. In 1907 the couple moved to St. Petersburg, but he had no chance at a permanent position in academia because he was an Austrian and a Jew. After arriving in St. Petersburg, Tatiana and Paul Ehrenfest made contacts with the younger generation of Russian physicists and mathematicians, including Jakov Davidovich Tamarkin (1888– 1945), Aleksandr Aleksandrovich Fridman (Friedmann; 1888–1925); the elder Orest Daniilovich Chwolson (Khvol'son; 1852–1934), Vladimir Andreevich Steklov (1864–1925), and Abram Fedorovich Joffe (Ioffe; 1880–1960). Joffe and Paul Ehrenfest (Pavel Sigismundovich, as friends called him in Russia) became close friends. Tatiana and Paul invited these physicists and mathematicians to an informal, unofficial colloquium that was held every other week at Ehrenfest’s home, where they discussed recently published works and other scientific subjects. The colloquium also was called the physics discussion club. Little is known about the work of the Ehrenfests in St. Petersburg; they spent five years there and although they made good friends, they were isolated as well. In that time both worked on their famous article, the review about statistical mechanics, which was published in 1911 in the famous Encyklopädie der mathematischen Wissenschaften. Felix Klein (1849–1925) edited the volume, and the Ehrenfests were familiar with him from Goettingen University.

Move to Leiden . Because of the political situation in Russia after 1911, the Ehrenfests, now with two little daughters, looked for better living and working conditions outside of Russia. In 1912 Paul Ehrenfest embarked on a two-month-long lecture and visiting tour through several German-speaking universities, including in Zurich and Prague, where he first met Albert Einstein (1879–1955). Finally, on the advice of Hendrik Anton Lorentz (1853–1928), Paul Ehrenfest luckily received an academic position: He was appointed as professor at the University of Leiden as Lorentz’s successor. In autumn 1912 the couple arrived in Leiden and remained there for the rest of their lives. Because of World War I, Paul obtained Dutch citizenship only in 1922; his wife probably did, too. Whereas each detail of the academic career of Paul Ehrenfest in Leiden is known—his research and his teaching activities, how he organized seminars and his famous colloquium Ehrenfestii (the Wednesday Physics Colloquium), how he managed the visits of all the important physicists of that time, including Niels Bohr (1885–1962) and his friend Albert Einstein—little is known about the scientific work of Tatiana in this period. From several letters it is obvious that she participated in the Wednesday discussions, and she was remembered as the intelligent partner of her husband. In 1931 she published her study on teaching mathematics problems, the Exercises in Experimental Geometry.

After Paul’s death in 1933, Tatiana had to independently care for the education and life of her three children, and she also began worrying about the developments in neighboring Nazi Germany. During the occupation of the Netherlands by German troops the Ehrenfest daughters survived all dangers (they were half Jews by Nazi definition). It seems from her list of publications that Tatiana could work in science again only after the liberation of the Netherlands in 1945. In 1956 and in 1958 her important articles on thermodynamics were published, in Leiden and in the American Journal of Physics, respectively.

Tatiana Ehrenfest-Afanas’eva belonged to the rare and small group of talented women mathematicians who luckily received professional training at universities in the beginning of the twentieth century and who worked in the fields of mathematics and science. Her marriage had a double and paradoxical effect on her career. Thanks to her husband she came in contact with many important physicists of her time, but she was mostly considered simply his wife, and his secretary or private assistant. It is difficult to reconstruct her ideas and her own scientific work. Thanks to such colleagues as Albert Einstein and Niels Bohr, the scientific work of Tatiana Ehrenfest was acknowledged in the 1920s, and thanks to colleagues such as Hans Freudenthal and E. J. Dijksterhuis, she was accepted as an intellectual in the 1950s.

Ehrenfest published several articles on different topics, first together with her husband, especially their famous article in 1911, but also alone, such on randomness (1956) and entropy (1958). She also wrote about methodological problems on the didactics of mathematics, and how to teach children mathematics and geometry (1931, 1960). The work of Tatiana and Paul Ehrenfest on the foundations of statistical mechanics and statistical thermodynamics was important to the development of those fields.

BIBLIOGRAPHY

WORKS BY EHRENFEST-AFANAS’EVA

With Paul Ehrenfest. “Bemerkung zur Theorie der Entropiezunahme in der ‘Statistischen Mechanik’ von W.Gibbs.” Wien Berichte 115 (1906): 89.

With Paul Ehrenfest. “Über eine Aufgabe aus der Wahrscheinlichkeitsrechnung, die mit der kinetischen Deutung der Entropievermehrung zusammenhängt.”Mathematisch-Naturwissenschaftliche Blätter 3 (1906).

With Paul Ehrenfest. “Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem.” Physikalische Zeitschrift 8 (1907): 311.

With Paul Ehrenfest. “Begriffliche Grundlagen der statistischen Auffassung in der Mechanik.” In Enzyklopädie der mathematischen Wissenschaften, Vol. 4, Teil 32, Leipzig, Germany: Teubner, 1911.

“Die Anwendung der Wahrscheinlichkeitsrechnung auf gesetzmässige Erscheinungen.” Journal der Russ.Physikalischen Gesellschaft 43 (1911): 256.

Exercises in Experimental Geometry. 1931. Available from http://www.pims.math.ca/~hoek/teageo/TEA.pdf

Die Grundlagen der Thermodynamik. Leiden, the Netherlands: E. J. Brill, 1956.

“On the Use of the Notion ‘Probability’ in Physics.” American Journal of Physics 26 (1958): 388.

With Paul Ehrenfest. The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, New York: Cornell University Press, 1959.

Wiskunde: Didactische opstellen. Zutphen, the Netherlands, 1961. A treatise on the teaching of mathematics, in Dutch.

OTHER SOURCES

Klein, Martin J., and Paul Ehrenfest. The Making of a Theoretical Physicist, Vol. 1. Amsterdam: North-Holland Publishing Company, 1970.

Kochina, P. Ja. Nauka, ljudi, gody. Vospominanija i vystuplenija. Moscow: Nauka, 1988. Memories of the female mathematician P. La. Kochina (1899–1999), who attended the women courses in St. Petersburg.

“References on T. Ehrenfest.” In Twentieth Century Physics, Vol. I–III, edited by Laurie M. Brown, Abraham Pais, and Sir Brian Pippard. New York: Institute of Physics Publishing and American Institute of Physics Press, 1995.

Annette B. Vogt