Sofya Kovalevskaya: A mathematical journey

1. Sofya Kovalevskaya: A mathematical journey 1850-1891 Veda Roodal Persad Thompson Rivers University (TRU) Kamloops, BC vroodalpersad@tru.ca BIRS March 2018

2. Phenomenon of Interest • Engagement with mathematics • In what ways do we (as human beings) react to/with mathematics? • What can we learn about the discipline of mathematics by studying engagement with mathematics? Who do we have to be in order to engage with it?Do we find mathematics or does it find us? • What does mathematics demand of us? What are the costs and rewards of engaging with mathematics?

3. Wherein lies mathematics? • Tony Brown (2008): Mathematics is accessed through the accounts of others. • Written accounts • Autobiographies of mathematicians • Biographies of mathematicians • Oral accounts • Interviews with mathematicians (both practising and retired)

4. Major Turns in the Mathematics Education Literature • Affect (McLeod, 1992) • Psychodynamics (FLM, 1993 edited by Dick Tahta) • The Psychoanalytic Turn (Brown, 2008, The Psychology of Mathematics Education: A Psychoanalytic Displacement)

5. The Construct of Desire • Bracher (1993), in Lacan, discourse and social change: A psychoanalytic cultural criticism, p. 19 • “Insofar as a cultural phenomenon succeeds in interpellating subjects—that is, in summoning them to assume a certain subjective (dis)position--it does so by evoking some form of desire or by promising satisfaction of some desire.” • For Lacan, desire is borne out of a lack in the subject, from alienation and separation, the méconnaisance or misidentification with the Other. • One of Lacan’s dicta: Desire is desire of the Other.

6. Desire is desire of the Other: Bracher’s Forms of Desire

11. Kovalevskaya’s Journey in Mathematics • Accomplishments • First woman in the world to receive a doctorate in mathematics • She won the Bordin prize for her work on the rotation of a solid body about a fixed point (1888) • Say what you know, do what you must, come what may.Motto on her paper "On the Problem of the Rotation of a Solid Body about a Fixed Point." • First woman professor of mathematics and mechanics at Stockholm University, Sweden • Second editor of the journal, Acta Mathematica, (the first was Mittag-Leffler)

12. How did it begin? Active anaclitic desire (to possess a means of enjoyment) • Stories from her uncle - quadratures, squaring the circle, and asymptotes • Happy occurrence: Wallpaper of notes of a calculus course; protracted attention • She writes of hiding an algebra textbook under her pillow and reading it through the night • She devised some trigonometry in order to understand a physics textbook written by her neighbour

13. She was smuggled in to classes at the university by men sympathetic to the cause • She journeyed through Europe seeking to be admitted to classes • She sought out Karl Weierstrass, became his student and then his colleague

14. Active narcissistic desire (devotion or identification with the Other) • She identified strongly with the style of Weierstrass in doing mathematics (he embodied the Other of mathematics for her) • She sought to be published in the two highly regarded mathematical journals at the time • She became the second editor and the first woman editor of a mathematics journal

15. Substitutes/Fake • Parented by her nurse (her mother to her nurse: “Take your savage away; she is not wanted here”) • A pretend fictitious marriage so that she could travel abroad to study mathematics • A surrogate father in Weierstrass (he referred to himself as her Spiritual father) • There was a false note to her life. In a letter to her sister, Anyuta: “In my present life, despite its seeming logic and completeness, there is a certain false note that I cannot determine, but which I feel nonetheless.”

16. Leitmotif of Asymptotic Desire • Lacan: Asymptotic desire, desire as a movement, always approaching but never obtaining an object of desire. • She had competing passions for mathematics and literature (an attempt to resolve the Imaginary and the Symbolic) • Hemmed in by the signifiers of ‘Russian’, ‘woman’, and ‘mathematician’ • Hers was a journey in search of that lost object, her old friend, the limit from the wallpaper

17. Mathematics as Fantasy • “I understand your surprise that I can work at the same time with literature and mathematics. Many who have never had an opportunity of knowing any more about mathematics, confound it with arithmetic and consider it an arid science. In reality however, it is a science which requires a great amount of fantasy, and one of the leading mathematicians of our century states the case quite correctly when he says that it is impossible to be a mathematician without being a poet in the soul.”

18. Her Trajectory • Kovalevskaya: “My destiny, or, if you wish, the main goal of my life, but I like more the word, destiny … I feel that my destiny is to serve the truth, that is science, and to blaze the trail for women, because that means to serve justice.” • The ultimate fantasy of mathematics for Kovalevskaya was that it was a place where she could find herself and that it was a place of truth. It turned out for her to be a place of both truth and power denied.

21. … to Mathematics Education • In order to educate mathematicians we have to awaken the desire • This research • extends the knowledge and the conversation on what is happening in our classrooms/what are we doing to our students/is mathematics for all? • raises our awareness of the personal and the psychoanalytical dimensions of the learning and teaching endeavour • Mathematics, like poetry, in its symbolic notation not simply notation or representation; metonymic processes and unaware connections such as with Kovalevskaya and the wallpaper • We have to pay attention to the mover that underpins the mathematical endeavour, namely, desire

22. Thank you! • Questions?