„ has been for me a source
of joy, of comfort and solace in times of crisis,
of independence and strength.”
Alexandra Bellow
Alexandra Bellow (née Bagdasar; previously Ionescu-Tulcea) was a Romanian-American mathematician who made important contributions to the fields of ergodic theory, probability, and analysis.
Alexandra was born in Bucharest, Romania, on 30 August 1935. Her parents were both physicians. Her mother, Florica Bagdasar (née Ciumetti), was a child psychiatrist, and her father, Dumitru Bagdasar, was a neurosurgeon. She received her degree in mathematics from the University of Bucharest in 1957, where she met and married Professor Cassius Ionescu-Tulcea. She accompanied her husband to the United States in 1957, where she received her Ph.D. from Yale University in 1959, under the direction of Shizuo Kakutani, with the thesis titled “Ergodic Theory of Random Series”. After receiving her degree, she worked as a Research Associate at Yale, as an Assistant Professor at the University of Pennsylvania, and as an Associate Professor at the University of Illinois at Urbana-Champaign. In 1967, she joined Northwestern University and became the first woman to hold the position of Full Professor of Mathematics at that university in 1968, a role she maintained until her retirement in 1996. At that time, she was appointed Professor Emerita.
On 24-25 October 2015, the Department of Mathematics at Northwestern University hosted a conference for women undergraduates in the mathematical sciences. A highlight of the event was her address, a condensed version of which was published under the title Flashbacks of a mathematical life in Notices of the AMS (Sept. 2016, 931-933). In this article, she remembers: “In parallel with the mathematical analysis course, Professor Solomon Marcus ran the analysis seminar, and in his spirited way exposed us to a wealth of concrete examples and problems that complemented and enhanced the theory.”
During her marriage to Cassius Ionescu-Tulcea (1956–1969), she and her husband co-wrote many papers and a research monograph.
Alexandra’s second husband was the writer Saul Bellow, who was awarded the Nobel Prize in Literature in 1976, during their marriage (1975–1985). In a 1980 interview with The New York Times, Saul Bellow was quoted as saying about Alexandra:
“She’s a wonderful woman. I’m used to looking at pieces of paper I’ve written and understanding them, but when I look at her mathematical papers, I’m puzzled”.
Alexandra features in Bellow’s writings; she is portrayed lovingly in his memoir, To Jerusalem and Back (1976), and, in his novel The Dean’s December (1982). Her portrayal was further developed in Bellow’s last novel, Ravelstein (2000), the tale of a friendship between a university professor and a writer, and the complications that animate their erotic and intellectual attachments in the face of impending death.
Alexandra advised many young women in mathematics, including to “stay with her maiden name, professionally”, observing that her identity as “Saul Bellow’s wife” sometimes overshadowed her own mathematical reputation.
The 1990s were a period of personal and professional fulfillment for Alexandra, marked by her marriage in 1989 to the famous Argentine-American mathematician Alberto P. Calderón.
Alexandra Bellow died in Chicago, Illinois, on 2 May 2025, at the age of almost 90.
Alexandra’s early work focused on the properties and consequences of lifting. The lifting theory, which began with the pioneering papers of John von Neumann and later Dorothy Maharam, gained prominence in the 1960s and 1970s with the work of C. Ionescu Tulcea and provided the definitive treatment for the representation theory of linear operators arising in probability. Their monograph, A. Ionescu Tulcea, C. Ionescu Tulcea, Topics in the Theory of Lifting, Springer-Verlag, 1969, has become a standard reference in this area.
In the early 1960s, Alexandra worked with C. Ionescu Tulcea on martingales taking values in a Banach space. Their work initiated the study of vector-valued martingales, with the first proof of the ‘strong’ almost everywhere convergence for martingales taking values in a Banach space with the Radon–Nikodym property; this opened the door to a new area of analysis, the ‘geometry of Banach spaces’. Alexandra later extended these ideas to the theory of ‘uniform amarts (asymptotic martingals)’, now an essential chapter in probability theory.
In the early 1980s, she initiated a series of papers that led to a revival of the area of ergodic theory, focusing on limit theorems and the delicate question of pointwise almost everywhere convergence. This was accomplished by exploiting the interplay between probability and harmonic analysis in the modern context.
I witnessed Professor Solomon Marcus many times saying that Alexandra is the best Romanian woman mathematician.
I met Alexandra Bellow in 2007 in Bucharest. Since then, we have had a frequent exchange of emails and telephone calls, primarily discussing mathematics and reminiscing about our time as students at the Faculty of Mathematics in Bucharest.
Alexandra Bellow, Cristian S. Calude, and Tudor Zamfirescu co-edited the book Mathematics Almost Everywhere: In Memory of Solomon Marcus, World Scientific, 2018, a collection of original research papers and surveys dedicated to the memory of our professor and mentor, S. Marcus (1925–2016).