#### by Alexandra Bellow Calderón

Alberto Pedro Calderón was born on September 14, 1920, in Mendoza, Argentina, a city at the foot of the Andes. With its strong desert climate, its eternally snow-capped mountains, its picturesque vineyards and olive orchards — where Alberto roamed freely as a child — Mendoza left an indelible imprint on Alberto’s imagination. He would return to Mendoza often later in life.

As a child, Alberto was determined to understand how things “really worked” He became good at fixing all sorts of things — mechanical, electrical, or otherwise. As an adult, Alberto was known among family and friends as “the man with the golden hands” because he could fix anything (be it a broken down Olivetti typewriter, a Swiss watch, an out of tune piano); in the process he fabricated the pieces that he needed and came up with the most unorthodox solutions.

Alberto acquired his early love for mathematics and music from his father, a physician, who, realizing his son’s unusual gifts, tried to stimulate him. “At the dinner table he would challenge Alberto, a boy of six or seven, to make rapid mental calculations; or, he would play classical music for Alberto and his sister.” To the end of his life Alberto could never listen to the Bach Partita in D minor, the Chaconne especially, with anything less than total absorption and rapt emotion. “The link between mathematics and music was there all of his life.” This makes one think of Leibniz’s famous saying: “Music is the secret arithmetic of the soul, unaware of its act of counting”.

There were, however, hurdles on the road to becoming a professional mathematician, “a mathematician’s mathematician”, as Alberto Calderón was sometimes called, because other mathematicians would come to him for help when they got stuck on a difficult problem.

“In the beginning, Alberto seemed destined for a career in engineering. His father wanted him to study in the best engineering school in the world, which at the time was ETH (Eidgenössische Technische Hochschule) in Zürich. In order to have him overcome the language barrier and get him ready for ETH, his father sent him, at the age of twelve, to a boarding school in Switzerland, the Montana Knabeninstitut near Zürich. It is here that Alberto met his destiny in the person of Doctor Save Bercovici, the mathematics professor. Their relationship began when Alberto committed a mischievous act in the presence of the professor. The traditional punishment was to send the culprit to his room for three days, during the hours when the boys used to go skiing. But the professor had a different idea. He saw this as a unique opportunity to attract Alberto to mathematics: he gave the boy a problem in Geometry, promising him that if he could solve it, he would be pardoned. The problem was to construct with ruler and compass only, an isosceles triangle, given the height and the sum of the length of the base and one of the sides. With youthful ambition and energy, Alberto set to work and found a construction that solved the problem. Alberto was pardoned, Prof. Bercovici became Alberto’s mentor and mathematics moved permanently to the center of Alberto’s mental life. Unfortunately, family money ran out, and after two years in Switzerland, Alberto was called back to Argentina.”

“Alberto and Dr. Bercovici did not see each other again until thirty years later. Alberto and his first wife, Mabel, were traveling in Europe, they passed through Zürich, and Alberto looked up Dr. Bercovici in the telephone book, finding his name, followed — as was the custom in Switzerland at that time — by a brief description of his professional activities. Dr. Bercovici was a colorful character and in his case the description read: ‘Mathematics, Physics, Philosophy, Psychotherapy.’ Dr. Bercovici remembered Alberto, his star pupil, perfectly well. It was a very emotional, somewhat chaotic encounter: the ladies conversed in English, Dr. Bercovici spoke in German and Alberto in French, since Dr. Bercovici understood French but could not speak it, while Alberto understood German but could no longer speak it.” Alberto did not tell Save Bercovici about his own academic accomplishments; he was too shy, or too modest, or perhaps he remembered too well how the old Mathematics Professor used to admonish the class: “Boys, please, do not brag! (bitte nicht protzen!)”. This was the last time that Save Bercovici and Alberto saw each other.

It is fair to say, however, that the two years that Alberto spent in Switzerland as a schoolboy, were a mind-opening, life-transforming experience that contributed in no small measure to the breadth of intellectual interests and quiet self-confidence that he exhibited all his life. A testimony to this is the following. When Alberto Calderón returned to Chicago from Buenos Aires in 1989, to accept a post-retirement appointment at the University of Chicago and to get married a second time, he came with only three suitcases: one of them contained his favorite papers and books (most of these books showed signs of wear and tear and had been carefully and lovingly restored by Alberto himself). Here is a partial list:

“A Thousand and One Nights”, with illustrations by E. Dulac (upon receiving first prize at the school in Switzerland, 1934)

Will Durant, “The Great Philosophers” (upon receiving first prize at the school in Switzerland, 1934)

J. Rey Pastor, “Análisis Algebraico”, Madrid, 1934

Rouché et [sic] Comberousse, “Géometrie”, Paris, 1900

A. Zygmund, “Trigonometrical Series”, First Edition, Warsaw, 1935

de la Vallée Poussin, “Cours d’Analyse Infinitésimale”, Paris, 1937

J. Marcinkiewicz, “Collected papers”, Warsaw. 1964

S. Saks and A. Zygmund, “Analytic Functions”, Warsaw, 1965

G. H. Hardy, “Collected papers”, Oxford, 1967

A book of tangos (the lyrics of the best known Argentine tangos). Alberto knew most of these tangos by heart. At home, when listening to tango music, after a glass of wine — preferably a good Malbec from Mendoza — he would sing along or get into the step, for he was a real “

*tanguero*”, the tango was in his blood.Alberto’s translation into English of several beloved poems from world literature (Alberto was fluent in several languages and loved poetry). Here is the translation into English, done by Alberto in the spring of 1989, of one of the best known poems of the great Spanish poet Gustavo Adolfo Bécquer (Rimas LIII, 938):

Again will dark swallows

hang their nest from your balcony,

and with their black wings

playfully call by your windowpane.

But those which slowed their flight

to contemplate your beauty and my bliss,

the ones that learned our names,

those won’t come again.

Again will vines and ivy

climb the walls of your garden

and perhaps bloom in spring

more beautifully than before.

But the dark leaves

covered with crystal drops of dew

we watched tremble, roll and fall

like tears of the day,

those leaves won’t grow again.

Again will your ears

hear passionate words of love,

and perhaps your heart

will wake from its slumber.

But, silent and ecstatic

as one prays to God in church,

the way I loved you, have no illusions

you won’t be loved that way again.

“Alberto finished high school in Mendoza. Persuaded by his father that he could not make a living as a mathematician, Alberto entered the University of Buenos Aires, studied engineering and graduated as a civil engineer. But being constant and persistent in his affections, he never abandoned mathematics — his great love. Having discovered the ‘Boletín Matemático Argentino’ in the library of his high school in Mendoza, Alberto, once in Buenos Aires, made the acquaintance of its editor, Dr. Bernardo Baidaff.” (Later Alberto liked to joke that the Romanians had played a crucial role in his life: the first one was Dr. Save Bercovici, the second one was Dr. Bernardo Baidaff, and the third one was his second wife, myself…). “Dr. Baidaff generously offered Alberto the use of his library and every assistance possible and this led to a lasting friendship. While studying engineering, Alberto established close contacts with the mathematicians at the University of Buenos Aires: he attended the advanced calculus classes of Julio Rey Pastor (the only Professor in the Institute of Mathematics), he participated in a seminar where he became acquainted with the brilliant young Spanish refugees Luis Santaló and Manuel Balanzat. He also met Rey Pastor’s assistant, the Argentine mathematician Alberto González Domínguez, a man of vast humanistic culture, who had left behind Greek, Latin, and philology for the sake of mathematics, and who became Alberto’s mentor, protector and devoted friend.”

“Alberto’s wish to become independent, to stop being a financial
burden to his father, led him, after graduating as a civil engineer,
to the state-owned oil company, the YPF (Yacimientos Petrolíferos
Fiscales), where he got a job in the research laboratory of the
geophysical division. The job suited him well: he had to work on
challenging, difficult problems in applied mathematics, having to do
with the design and use of instruments for geophysical prospecting.
This was in line with Alberto’s mode of thinking, for he firmly
believed that mathematics is the Queen of Sciences, and that any good
queen has to serve her subjects well.” It was in this Lab, in fact,
that Alberto conceived of the possibility of determining the
conductivity of a body by making electrical measurements at the
boundary; he did not publish his results until several decades later,
in 1980, in his short Brasilian [sic] paper, which pioneered a whole new
area of mathematical research on “inverse problems.”1
Alberto’s
independence of spirit and exceptional performance, however, annoyed
the lab director, who became enraged when he discovered that, in his
spare time, Alberto was *passionately* reading
Kuratowski’s
“*Topologie*.”
“Alberto finally, and very reluctantly, resigned. It was a blessing in
disguise, Alberto used to say later, that his lab director made life
difficult for him, for otherwise Alberto, who enjoyed his work, would
have very likely remained there for the rest of his active life.”

As it turned out, this unfortunate episode fortunately led to Alberto becoming a professional mathematician and to his spectacular mathematical career and fame. “Upon resigning his job at the YPF, he got an appointment at the Institute of Mathematics of the University. Soon after that, when Antoni Zygmund, the famous analyst from the University of Chicago, came to visit the University of Buenos Aires in 1948, Alberto was automatically assigned to Zygmund as his assistant.” A great mathematical talent was waiting to be “discovered.” The rest of the story is, if not history, certainly mathematical history, and is eloquently told in the next chapter.

As Alberto’s wife, I shared with him the last nine years of his life (his last Chicago period) and worked with him too, so perhaps some details about Alberto’s style of doing mathematics would be in order:

It was sheer joy to discuss a mathematical problem with Alberto, for his mind never traveled the beaten path and could move with great ease from a concrete problem to the most sophisticated abstract setting. He seldom read other mathematicians’ papers or books. If he learnt of a new theorem that interested him, he would try to prove it by himself and the techniques that he developed in the process would often have unexpected, far-reaching consequences elsewhere. This was the search for knowledge at its most authentic and inspiring.

Alberto seemed to be oblivious to mathematical prejudices and fads. He was simple and reserved in his manner; he treated colleagues and students alike with kindness and respect. His openness and generosity in sharing mathematical ideas were legendary.

Alberto Calderón had strong emotional and mathematical ties with his native country, Argentina, and with Spain as well, but his enduring “mathematical home” was undoubtedly the University of Chicago, an institution he respected, admired and unequivocally loved all his life long.

The year we were married, 1989, turned out to be a kind of “International Calderón Festival,” for Alberto received a lot of recognition that year: the Wolf Prize (from Israel), the Premio de Consagración Nacional (from Argentina), the Steele Prize (from the American Mathematical Society). What an unusual “dowry” to bring to a marriage — friends mused. I knew that Alberto regarded society’s insatiable appetite for fame and immortality with benign amusement and a touch of irony. When I marveled at how he could remain so unassuming despite all the acclaim, he would simply answer “I know how little I know”. It was the answer of a mathematician’s mathematician.2