**Alberto Calderón** was an Argentinian mathematician who cooperated with Zygmund to found the Chicago school of "hard analysis".

- Alberto Calderón began his education at the Colegio Marista San Josee de Mendoza.
- Their relationship began when Alberto committed a mischievous act in the presence of the professor.
- 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.
- 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 centre of Alberto's mental life.
- Education at the Institut Montana Zugerberg was expensive and Pedro Calderón could not afford to keep Alberto at the school so after two years he returned to Argentina to complete his secondary schooling at the Agustín Álvarez National College in Mendoza, Argentina.
- There he met Bernardo Baidaff, the editor of the Boletín Matemático Argentino, who helped Calderón continue his mathematical interests.
- While still an engineering undergraduate, he attended calculus lectures by Julio Rey Pastor, and got to know his assistant Alberto González Domínguez.
- Calderón attended the mathematics seminar where he got to know Luis Santaló and Manuel Balanzat.
- Calderón resigned but he did so reluctantly since he had enjoyed the work.
- He was able to get a job in the Institute of Mathematics at the University of Buenos Aires and began research in mathematics under the supervision of Alberto González Domínguez.
- In 1948 Antoni Zygmund visited the University of Buenos Aires and began to discuss various problems with Calderón.
- Zygmund posed Calderón a question and the puzzled Calderón replied that the answer was contained in Zygmund's own book 'Trigonometric Series'.
- Zygmund disagreed: what transpired was that Calderón only ever read the statements of the results, preferring to give his own reasoning and proofs...
- This originality was to be the hallmark of Calderón's work in the years to follow.
- This seminar was attended by González Domínguez, Calderón, Mischa Cotlar, and three other young Argentine mathematicians.
- Finally, he interrupted Calderón abruptly to ask where had read the material he was presenting, and a bewildered Calderón answered that be had read it in Zygmund's book.
- Zygmund vehemently informed the audience that this was not the proof in his book, and after the lecture took Calderón aside and quizzed him about the new short and elegant proof.
- Calderón confessed that he had first tried to prove the theorem by himself, and then thinking he could not do it, had read the beginning of the proof in the book; but after the first couple of lines, instead of turning the page, had figured out how the proof would finish.
- Calderón was awarded a Rockefeller Scholarship to enable him to undertake research at the University of Chicago and this he did working with Zygmund.
- It was never Calderón's intention to write a Ph.D. dissertation since he wanted to do research and not spend time putting together a thesis.
- One day Marshall Stone, chair of the mathematics department at the University of Chicago, asked Calderón to come to his office bringing his published papers.
- Stone picked up Calderón's three single author papers, stapled them together, and said "This is your thesis!" It was an outstanding thesis for which Calderón was awarded his Ph.D. in 1950.
- Pablo Calderón was awarded a Ph.D. from New York University in 1990 for his thesis On the macroscopic behaviour of a large stochastic system.
- From 1950 to 1953 Alberto Calderón was an associate professor at Ohio State University, then he spent 1954-55 at the Institute for Advanced Study at Princeton.
- Mabel Calderón died in Buenos Aires in August 1985.
- In 1989 Calderón returned to the University of Chicago and worked there on a post-retirement appointment until 1992.
- The year 1989 was significant for Calderón in another way.
- Calderón, then a professor at the Massachusetts Institute of Technology, "had a magnificently large office, in keeping with his mathematical stature.
- There was a shortage of office space in the Mathematics Department and the Chairman asked Alberto if he would mind sharing his office with a visitor.
- While Calderón was both architect and bricklayer, his lectures emphasised the bricks.
- An irked but calm Calderón, along with the audience, would seek to bridge the gap.
- Calderón was rethinking the theorems on the blackboard before us; we were expected to think along with him.
- Cora Sadosky was one of Calderón's Ph.D. students at Chicago.
- Calderón, on the other hand, with his background as an engineer, saw that such operators held an important key to understanding the theory of partial differential equations.
- Out of these differing points of view was born one of the predominant intellectual movements in 20th century mathematics: the Calderón-Zygmund theory of singular integral operators and the Calderón-Zygmund school devoted to their study.
- In particular Calderón wanted to describe a calculus for elliptic differential operators and, from this beginning in the 1950s, the theory of pseudodifferential operators grew in the 1960s.
- In 1958 Calderón published one of his most important results on uniqueness in the Cauchy problem for partial differential equations.
- The American Mathematical Society also awarded Calderón their Bôcher Prize in 1979 and he had previously been American Mathematical Society Colloquium Lecturer in 1965 when he spoke in Ithaca on Singular Integrals.
- Argentina gave many honours to Calderón.
- This was partly because Calderón made many visits to Argentina to give lectures and to help with advising Ph.D. students.
- Calderón was elected to the American Academy of Arts and Sciences (1957), the National Academy of Exact, Physical and Natural Sciences of Argentina (1959), the National Academy of Sciences of the United States (1968), the Spanish Royal Academy of Sciences (1970), The Latin American Academy of Sciences of Venezuela (1983), the French Academy of Sciences (1984) and the Third World Academy of Sciences (1984).
- Calderón's techniques have been absorbed as standard tools of harmonic analysis and are now propagating into nonlinear analysis, partial differential equations, complex analysis, and even signal processing and numerical analysis.
- Although this influence will continue to be felt, despite writing around 80 mathematical papers, Calderón never wrote a monograph on his highly original ideas.
- Mathematically Calderón was exceptional not only for the strength of his talent but for his peculiar way of grasping mathematics.
- Although he was an individualist to the core, he influenced profoundly the work of others, who developed what is known as the "Calderón program".
- Calderón was modest, sure of himself, and quite indifferent to competition.

Born 14 September 1920, Mendoza, Argentina. Died 16 April 1998, Chicago, USA.

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Origin Argentina, Prize Wolf

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive