October 2022

On Automathographies

Please reference as: Maria Tamboukou (2022) 'On Automathographies' , https://sites.google.com/view/numbersandnarratives/newsletter/october-2022

‘I like words more than numbers and I always did’ (1985, 3), Paul Halmos wrote in the very first pages of his ‘automathography, a mathematical biography written by its subject’ (3). In Halmos’ view, an automathography should not be conflated with an autobiography, ‘the story of my origins and my life’ (3). But is there such a divide or separation possible? Throughout his book Halmos refers to childhood memories, desires, relations with significant others, impressions of places and spaces, as well as political and cultural events that shaped his desire to become a mathematician. Books and languages play a significant part in his automathography: ‘I read a lot, write a lot, and love languages—and I suppose at bottom it all comes down to liking words’ (8) he has emphatically written, highlighting the importance of culture in his automathography. As George Sarton has importantly argued, ‘the history of mathematics should really be the kernel of the history of culture’ (1936, 4). Halmos is adamant that to become a mathematician, ‘you must love mathematics more than anything else’ (1985, 400). Pure love is not enough of course, ‘you must work at it hard and without stop, and you must never give up’, he has further noted. (400) And yet when it comes to the hierarchy of existential needs, desires and strives, the love of mathematics comes first: ‘I am not saying that the love of mathematics is more important than the love of other things. What I am saying is that to the extent that one’s loves can be ordered, the greatest love of a mathematician (the way I would like to use the term) is mathematics’ (401). Halmos’ automathography is written from the perspective of a male mathematician who followed the networks and opportunities available to his gender in the long run of the twentieth century. This does not mean that he did not face the prejudices of being a Jewish immigrant and of carrying his Hungarian accent, despite the fact that he was educated in the USA: ‘Then there was the accent. I was a foreigner, with or without pejorative adjectives, I felt like one, and I sounded like one’, Halmos has poignantly noted (1985, 15). And yet, while reading his automathography I often wondered how different things would be for a woman becoming a mathematician in the same period. In Chapter Six of his automathography, Halmos fondly remembers the Institute for Advanced Studies at Princeton University, where he became of age as a mathematician:

The Institute was a small, cozy operation when I arrived in Princetonin 1939. The center of the life of all the mathematicians in Princeton,both University and Institute, was Fine Hall (the old Fine Hall), whichis still my Platonic ideal of a mathematics building. Dark corridors,leaded windows, heavy furniture, worn carpets; the common room alwaysopen, always in use; the library up to date, complete, run with an ironhand by Bunny Shields, tiny, white haired, probably born looking as ifshe were in her late 50’s, severe, but always helpful. (Halmos 1985, 84)

Halmos has written that he would ‘virtually lived in the common room’, where ‘early morning or the middle of the night, there was always someone there, and some conversation about mathematics, the war, the quirks of the big shots, or the best nearby restaurant for oyster stew was always going on’. (85) There were no such opportunities for knowledge and networking for women mathematicians, since Princeton only admitted women in its graduate courses in mathematics in the late 1960s. (see Schafer 1987, x) Even when women were admitted, they would not always feel welcome and at home. As Alice Shafer has poignantly commented, ‘at Harvard University, some professors refused to allow women to sit in their classrooms. They were however allowed, to sit in chairs placed just outside the classroom doors, so that they could hear the lectures.’ (x)

Despite such harsh gendered restrictions, which went on beyond the middle of the twentieth century, the love that Halmos has written about, seems to surpass gender, time and geographical boundaries. In her long engagement with Sofia Kovalevskaya’s life and work, Russian mathematician Pelageva Kochina has chosen ‘Love and Mathematics’ as an encapsulating title for the scientific biography of the first woman to hold a chair in mathematics in modern Europe. (Kochina 1985) But what does it mean to love mathematics, how is the love of mathematics expressed in women mathematicians’ ego documents and how can we map its socio-economic, cultural and political conditions of possibility? In addressing these questions, I have configured the plane of my research in the intersection or rather entanglement of mathematics with philosophy, literature, poetry, but also social activism. In gendering Halmos’ notion of automathographies’, what I argue is that working auto/biographically with women mathematicians is a way of better understanding not only the gendered micro histories of the discipline, but also and perhaps more importantly the slow process of the long way to gender equality, which is still unfolding in our days. In this light automathographies become an important tool in what drawing on Michel Foucault (1986), I configure as ‘counter-memory studies’ — a turn to the past as a way of reconfiguring the present and prefiguring the future of women in mathematics.

References

Foucault, Michel. 1986. ‘Nietzsche, Genealogy, History.’ Translated by Donald. F. Bouchard and Sherry Simon. In The Foucault Reader, edited by Paul Rabinow, 76-100. Harmondsworth: Peregrine.

Halmos, Paul. 1985. I want to become a mathematician: an automathography. New York: Springer.

Kochina, Pelayeva. 1985. Love and Mathematics: Sofia Kovalevskaya. Transl. Michael Burov. Moscow: Mir Publishers.

Shafer Alice. 1987. ‘Foreword’ In Women of Mathematics: A Biobibliographic Sourcebook, edited by Grinstein, Louise, S and Paul, J. Campbell, ix-xii. New York: Greenwood Press.

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