A Memoir: Agnes Berger (1916-2002) and
Our Friendship
Miriam Lipschutz
Yevick
Soul-mates
Agnes and I were soul
mates from the start. We had both earned Ph.D.’s in mathematics, Agnes at the
University of Budapest under Professor Feher in 1939 and me at M.I.T in the fall of
1947. Agnes at 23 made her escape on her own after the war’s outbreak via Berlin to
take one of the last boats, the Serpa Pinta, from Portugal to the U.S. My father,
transformed by panic from his usual indecisiveness, had led my family in flight from
Belgium to the U.S. via Portugal in the months after the Nazi invasion of Belgium. The gruesome fate we had
been spared cemented our bond. We also shared the recognition that our love of mathematics
had helped to give us a new lease on life.
We met in the fall of
1947 in the Columbia Mathematics library, a four-flight climb up the rotunda. We were in
the same situation: women Ph.D.’s in mathematics without a position because of our
gender. Upon her arrival in the U.S. Agnes had approached von Neumann, an acquaintance
from Hungary, for advice on how to further her career. He suggested—even though a
decade later he wrote a letter of recommendation in which he spoke very highly of her
abilities—that she should work as a housekeeper and do mathematics at night. I had a
similar experience upon earning my degree at MIT. The woman in charge of placing women
graduates informed me that “of course I could not get an academic position in
mathematics as a woman” and that I should opt for being a technical assistant.
However, not long after her arrival, Agnes had “captured” (in Erdös language)
Laçzy, a successful stockbroker. “Something was happening,” she told me later,
so she concentrated on her goal of establishing a family, which also had interfered with
her ambitions. Yet we each were determined to stay with our vocation, so we dragged
ourselves uptown (I lived in Hoboken, Agnes on the East Side) and up the stairs. We
faithfully attended seminars, we studied the books, we attempted to do some research on
our own and we wondered about what, as women, we should do with our lives. Agnes had a
two-year-old toddler at home and wanted another baby. [1] In
the face of our ambivalency, we supported each other in our work.
Agnes’ First Papers
In spite of the
difficulties, Agnes’ first paper was accepted in 1948 and appeared on page 25 of the
first issue of the Proceedings of the AMS.
“On disjoint sets of distributions” was in the company of articles by such
luminaries as Fuchs, Renyi, Harris Chandra, Erdös, Gleason, Dieudonné, Otto Szasz….
She
had begun her study of statistics; her article was motivated by a question raised to her
by George Wald, the creator of Sequential Analysis. This
paper already displayed her imaginative use of mathematics in tackling applied problems.
At that time, many mathematicians looked upon statistics as an “inferior”
discipline; Agnes applied statistical methods only after deriving an appropriate and
precise mathematical foundation. Her correspondence and collaboration with Jerzy Neyman
testify to her role in the development of mathematical statistics. Agnes was motivated by
her strong wish “to make a contribution.” She loved mathematics, but she wanted
science to connect with social good. She wanted mathematicians and statisticians to have a
social conscience, to relate to science and social responsibility.
I shared her outlook. I
had done my thesis in measure theory and the mathematician Yael Dowker, whom I had
befriended in Cambridge, suggested that I work in probability theory to be better able to
do some practical things. In fact this led me to an interest in the dichotomy between
limit laws for sums of independent random variables tending either to normality or to
another type of stability, a subject superbly presented by Paul Levy in his Theory des Probabilités. This dichotomy was based
on the relation between the individual components to the sum; the first develops when
the components are uniformly negligible against the sum, the second when one or a few
individual components are dominant in the sum, as is the case in the distribution of
wealth and income. I also recall that during those years while accompanying my husband to
a physics symposium in Michigan, I asked Feynman to suggest a problem in probability
that would be “useful.” He advised me to work on problems “because they
were interesting.” I learned later on that the philosophy of “Science for the
sake of Science,” which he himself surely did not adhere to, was first espoused by
Bismarck, who found it a useful tool for controlling scientists.
Vignettes
Agnes and Laçzy rented
a summer cottage when Johnny was five, the Sommerfrische
a city child needed. Agnes felt rather out of sorts as a vacation mother with no
opportunity to do her own work. She invited me for a weekend. The weather was balmy and
the mosquitoes out in force, the moon was full. “A great night for making love,”
Agnes whispered to me. However Johnny together with a group of age-mates had discovered
a machine from which freely gushed Coca-Cola. The whole pack, high on the drink,
rampaged all over the colony. They were eventually subdued and the night was still
long.
One day I gave a
lecture at the Columbia Statistics seminar in which I held my ground against some
notable in the audience who did not understand me and harassed me. “I admire your
courage in talking back,” Agnes said to me. This critic
called me to his office and sweated as I once more explained myself in
greater detail. “Why must you do such hard things?” he
finally lamented. A newcomer in the department, later Professor at Harvard, shared the
office with this mathematician. The newcomer
listened to my argument and showed the notable critic that my conclusions were correct.
I met Agnes in the corridor and praised my supporter to Agnes.
Agnes, who could be a flirt in the European upper-middle-class tradition, exclaimed:
“Now, Miriam, I
have an eye on him. Don’t you dare!” she exclaimed. She was equally sympathetic to my romantic dilemmas. “You must decide, Miriam, who you want to be the
father of your child,” she said to me at a critical juncture. Her words, spoken as
we ate in the Columbia cafeteria, still ring in my ears as I think of that fateful choice.
My son, David, was born
in 1954, when Johnny was nine. We lived in a small Manhattan apartment, and Agnes came
with Johnny to visit. After they left, John, to whom she unsuccessfully had been trying to
explain the term “bourgeois” said: “Now I understand what you mean. Miriam
and George are not bourgeois.”
Agnes moved to
Riverdale for the sake of the “frische
Luft” (fresh air) for Johnny. Each of our visits there was a joy. The company
always was unforgettable: economists, physicists, mathematicians and philosophers. The
food was unmatched, the pastry divine (we always looked forward to whatever Laçzy found
in the Hungarian shops). The same was true when they moved to her apartment in the city a
number of years later, when she announced: “we have come back from exile.” I
fondly remember my banter with Laçzy, in his eyes my naïve radicalism vs. his sensible
conservative views. In fact I deeply regret not following his financial advice, since we
always foresaw the demise of capitalism.
For five years after
Agnes’ father died she looked after her mother with a rare filial devotion. The image
of Mrs. Hollow in her somewhat gloomy Lexington Ave. apartment and Agnes fussing over her,
making her arrangements with the help, buying her food, trying to keep her entertained
with books, is inscribed in my memory with great admiration. (And inspired me when I was
in the same situation). Yet Agnes told me: “for my mother those six years after
father died were wasted years.” Later on I remember joining Agnes and her husband
for walks in the park when Laçzy was no longer in good shape; Agnes helped him with great
kindness and devotion.
Friend and Colleague
These were very
fruitful and creative decades for Agnes (in spite of her family obligations). She had been
appointed Instructor (1952–54), Assistant Professor (1957–64) and finally
Associate Professor (1964–93) in Biostatistics at the Columbia University School of
Public Health. In 1988 she was named Professorial Lecturer in Biomathematical Sciences
at Mount Sinai Medical Center. Her many publications ranged over a wide spectrum of
applications, while she simultaneously continued to develop theoretical methods to further
her investigations. To mention but a few of these articles: “The influence of the
thermal environment upon the survival of newly born premature infants,” Pediatrics, 1958. “On the question of whether
a disease is familial,” Journal of the
American Statistical Association, 1961. “On estimating recessive frequencies from
truncated samples,” Biometrics, 1967.
“Malignant melanoma in spouses,” Cancer
Research, 1979. “The relation of female polygamy to ganatrophic activity in the
rook strain of Aedes Aegypti,” Mosquito News,
1980.
Most of her work was
done in collaboration with colleagues. She always stressed her preference—in contrast
to my own—of talking a problem through with others, rather than writing. The
mathematics was sometimes simple, more often her reasoning was based on subtle
sophisticated arguments. The arguments were always rigorous; she would not brook any loose
ends. She often discussed her current finds with me, but I was not well enough versed in
the subject to understand without some reminders of the background of her work.
I was greatly impressed
with how she mixed pure mathematics with these concrete applications. Knowing her worship
of Latin, I was also quite amused by her use of the Latin expression mutatis mutandi in her exposition. She was an
excellent expositor and teacher, if highly demanding of rigor and logical precision of
thought in her students and interlocutors (like me).
I had become interested
in the subject of holography as a result of my correspondence with physicist and friend
David Bohm. I published “Holographic or Fourier Logic” in the journal Pattern Recognition, which interested Agnes very
much – except that she always was pressing me for foolproof definitions. This work
triggered an interest in the foundations of logic, and she gave me moral support as I
attempted to get some controversial conclusions published. She knew that it was hard to
break through when “thinking different,” as had been the case with David Bohm.
She did, however, balk at trying to understand Gödel’s theorem, with the comment
that von Neumann remarked that some parts of logic were the only “mathematics”
which made him feel that he was going crazy.
Later Years
After Laçzy died,
Agnes became much more outspoken politically, and I was delighted to see her shift in a
very articulate way to the left, perhaps inspired by John, an environmental writer. She
was also acutely aware of the injustices around her in the city and the world and asserted
with clairvoyance: “Why should we expect that our good life in this country will go
on as before while most of the rest of the world is mired in poverty? The time of
reckoning will come.”
She explained her
deeper involvement with another unforgettable comment: “When Johnny was a baby, I
came to love all babies; when he was a child, I came to love all children; when he was a
youngster, I learned to love all youngsters; and now I love everybody.”
For many years I drove
to the City from New Jersey to visit my parents on the Upper West Side. I would call Agnes
in the evening and ask: “Can I come?” She would say “yes” with
delight. It was a joy to see her at her door down the long corridor and enter a scene
reminiscent of my parents’ home in my childhood, the solid European furniture, the
fine rugs, the cyclamens and violets on her window sill, and to
drink her good coffee prepared in her inimitable style: boiled till the water rose and
then poured through a sieve. There was no end to what we talked about: politics,
mathematics, colleagues, our research, music, science, children, grandchildren, and
the lamentable state of American Culture to which they were exposed.
Agnes continued her
professional work even after she retired. Her publications include several written after
she turned eighty. Meanwhile I had been talking to her about the Foundations of Quantum
Mechanics to which my reading had returned after almost fifty years. I told her about an
error in von Neumann’s proof of the non-existence of hidden variables in quantum
mechanics. This proof had been of great importance in validating Bohr’s
interpretation of quantum mechanics among physicists versus Einstein’s views. A woman physicist, Grete Hermann had pointed out this error in a
publication in the late nineteen thirties, but her paper was completely ignored. [2]
Agnes, in spite of her general support of those challenging orthodoxy in science, refused
to believe that von Neumann could have made a mistake. It was only after I sent her one of
John Bell’s papers confirming the error that she admitted to her unjustified
obduracy. This discussion between us took part during the last years of her life. Two
years ago, in an attempt at understanding how probability is used in Quantum Mechanics, I
brought her a paper on this subject by a Professor at Cornell that I could not understand.
Even though it was by then hard for her to read, she made the effort. “Rubbish!”
was her opinion, as was my suspicion. If only in her honor, I am determined to prove her
right in this matter. I am still working on it.
In Memoriam
Agnes was an
intellectual in the deepest sense of the word, in the spirit of the outstanding scholars
Hungarian Jewry produced. She knew that her roots were in the Jewish tradition of learning
even if the learning had become secular, as were the roots of her profound social
conscience. She carried the burden of the world on her shoulders, as she believed all Jews
should. Agnes had an admirable scientific objectivity in all her judgments. Her voice was
truly authentic. She was ein Kultivierter Mensch,
as her parents and mine used to say.
I visited Agnes for the
last time in November 2001. Somehow the conversation turned to Latin, and I told her that
I never liked the Latin I studied in High school in Europe. This elicited a passionate
response. She quoted Ovid at great length; she hailed the importance of teaching children
to recite poetry, preferably in Latin; I was subjected to a procession of Latin
quotations. Then, changing the subject, she gave me medical advice. I had a recent
operation and was not feeling well. “If this was one of your family members, you
would take them to the best specialist. I want you to see the best specialist.” She
urged me on and on until I agreed I would do so (I haven’t yet).
Her vision was very bad
and she knew that she needed more help. Yet she was reluctant to make other arrangements.
I sent her the person who had taken care of my mother, but she was too anxious and
indecisive to act. I was worried when I left her. She would not hear of giving up her
independence to join John and his family in California. I did not speak to her again after
that evening; she died in March 2002.
Agnes’ phone
numbers is one of the few stored in my head for more than
forty
years: Regent71523. It no longer responds. Agnes is a voice inside me, which reminds me
“that we are all in all.” Losing Agnes is losing a part of myself. I think that
the greatest tribute her friends can pay her is to keep that voice alive.
__________________________________
[1] Laçzy maintained that he “was too old.” I
remember well the occasion when John, aged four perhaps, overwhelmed his gentle father who
refused to give in to his demands, by exclaiming: “You are a mean lion!”
[2] Hermann, G. Die naturphilosophischen Grundlagen der
Quantenmechanik, Abhandlungen der Fries’chen
Schule (6) (1935), 75-152. See also: Jammer,
Max, The Philosophy of Quantum Mechanics, John Wiley & Sons, New York, 1974. Cronin, Jane, Social Influences on Quantum
Mechanics, The Mathematical Intelligencer, 23, 4,
(2001), 15.
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