Rolando Chuaqui Kettlun

Quick Info

30 December 1935
Santiago de Chile, Chile
22 April 1994
Santiago de Chile, Chile

Rolando Chuaqui was a Chilean mathematician who trained first as a medic before turning to mathematics. He was an active researcher and important figure in the development of mathematical logic in Chile.


Rolando Chuaqui Kettlun was the son of Basim Chuaqui (1903-1992) and Georgina Kettlun (1916-2009). Basim Chuaqui was born in Homs, Syria but emigrated to Chile where he met Chilean born Georgina Kettlun. Rolando, the subject of this biography, was the second of his parents' six children, the first child, Wilberto, died at the age of eleven. Chuaqui studied at the National Institute school in Santiago de Chile. This school, officially known as Liceo Ex A-0 - Instituto Nacional General José Miguel Carrera, had been founded in 1813 and was, at the time Rolando studied there, probably the leading high school in Chile. He excelled in all his academic subjects at the National Institute but he totally lacked manual dexterity so he was [13]:-
... an outstanding student except, despite his efforts, in gymnastics and especially in everything that had to do with hand dexterity: drawing and handicrafts were almost torture for him. ... That clumsiness, known to lesser degrees in other members of his paternal line, was graded in a singular fact: as a child he decided one day to sleep with his shoes on so as not to have to tie them again. It is not known how many times he had slept like this until the night his mother surprised him.
He took the admission tests for both the Pontifical Catholic University of Chile and for the University of Chile, did extremely well, and both offered him a place. He chose to study medicine at the University of Chile and entered in 1953. It is reasonable to ask why he chose to study medicine rather than mathematics. The first point must be that his mathematics teachers at the National Institute did nothing to inspire him and, having found all academic subjects easy, he had a broad choice. He seems to have been drawn to medicine partly because he had relatives who were medics, and partly because medics were considered to be of high social rank.

His first two years of study went well and his performance in the examination was top class. In his third year he was offered private classes on the foundations of mathematics given by Carlos Grandjot. Thinking this would provide a more rigorous basis for some of the medical decisions he was expected to make, he gladly accepted.

Karl Grandjot (1900-1979) (known as Carlos Grandjot in Chile) was a German who had studied mathematics at the University of Göttingen and was awarded a doctorate in 1922 for his thesis Über das absolute Konvergenzproblem der Dirichletschen Reihen . He had been advised by Edmund Landau [12]:-
Dr Grandjot, as his students called him, arrived in Chile on the 1 May 1929, from Germany, hired by the Government to "provide his services as a Mathematics Professor in the educational establishments of the Republic. He would have the obligation to serve up to fifteen hours a week of classes, including seminars." Upon arriving, he began teaching "classes on Higher and Elementary Mathematics, Philosophy and Physics at the Pedagogical Institute of the University of Chile."
For more information about the development of mathematics in Chile and in particular of Grandjot's contribution to it, see THIS LINK.

Grandjot began the course which Chuaqui attended with logic and recommended Alfred Tarski's book Introduction to Logic and to the Methodology of Deductive Sciences (1936) and Willard Van Orman Quine's book Methods of Logic (1950). Chuaqui found these books easy reading and then progressed to Rudolf Carnap's Der logische Aufbau der Welt (1928). Chuaqui was greatly impressed by Carnap's book even though, since he did not know German, he could only approach it from a poor translation. After the logic lectures, Grandjot's course moved on to non-Euclidean geometry and looked at the work of János Bolyai and Nikolai Ivanovich Lobachevsky. Chuaqui began to build a library of mathematics books, which the local bookshop run by the mathematics professor Oscar Martín was able to import for him. He added books by Hilbert, Carnap, Quine, Russell's Principia Mathematica, and others, to his collection, reading them as soon as he was able to purchase them [13]:-
Rolando led a quiet and orderly life, logic and mathematics consumed almost all his free time, but there was always something left for reading a religious subject, going to mass with devotion and for music.
Despite devoting much time to mathematics, he continued with his medical studies but he found them increasingly requiring memorising material and no opportunity to apply logical deduction. He did further courses with Grandjot who taught him some number theory and modern algebra. After studying groups, rings, ideals, and fields, Chuaqui commented that mathematicians used easy words for difficult ideas, while doctors used difficult words for easy ideas. Grandjot recommended that Chuaqui should study differential and integral calculus but said that he would not teach that. He suggested that for calculus Chuaqui should take some lessons from Egbert Hesse who was a young lecturer in the School of Engineering at the University of Chile. He only took a few lessons but he acquired Richard Courant's two volume work Differential and Integral Calculus and soon he had completely mastered volume one. Perhaps Chuaqui's favourite book was Carnap's Introduction to Semantics and Chuaqui gave a talk on this book to the Chilean Society of Symbolic Logic, Philosophy and Foundations of Mathematics which had recently been founded by Gerold Stahl, professor of Classical Logic and Symbolic Logic in the Department of Philosophy [13]:-
In the 6th year Rolando had made a double decision: on the one hand, to dedicate himself to mathematics and, on the other, to finish his medical degree.
He graduated with an M.D. from the University of Chile in 1960 and then decided that he wanted to undertake research for a doctorate at the University of California at Berkeley where there was a Logic and Methodology of Science group with members from the three departments of mathematics, statistics and philosophy. He had had no formal studies in mathematics but Carlos Grandjot wrote a strong letter of recommendation. Chuaqui worked as an assistant lecturer in biochemistry while he waited for a decision from Berkeley. He received a conditional admission to the Logic and Methodology of Science programme and, with the award of a University of California-University of Chile Cooperative Fellowship, began his studies at Berkeley in 1961.

Chuaqui married Kathleen Ellen Henderson (1942-2014) in Westwood, Los Angeles, California on 17 August 1963. Kathleen was the daughter of John Dale Henderson (1903-1982), a librarian, and Ethel McGough (1902-1983). She was born on 8 July 1942 in Sacramento, California, the youngest of her parents' three children. Rolando and Kathleen Chuaqui had five children, four sons and a daughter.

At Berkeley Chuaqui was advised by David Blackwell who had been appointed to a professorship at the University of California at Berkeley in 1954. By this time Blackwell's interests had turned towards statistics and in 1956 he became Chairman of the Department of Statistics. He advised Chuaqui who submitted his Ph.D. thesis A definition of probability based on equal likelihood in 1965. The Introduction to the thesis begins [3]:-
The calculus of probability is applied to happenings or occurrences. That is, to situations that involve some change. Some of the situations are experiments or observations, such as: the tossing of a coin once, the tossing of a coin 100 times, the arranging of a deck of cards, the computing of the nth digit of the decimal expansion of π, the observation of the lifespan of a radioactive atom or a person, the selection of a sample of people and the observation of the number of left-handers in it. Others are natural phenomena, such as: the birth of a baby, telephone calls, accidents, the diffusion of a particle.

The essential element in all these examples is change. There is an initial state of affairs that changes to another state of affairs. I shall call all situations of this sort experiments. What we are interested in, in all experiments, from the point of view of the calculus of probability, is the result or outcome of the experiment. We want to know what the outcome of the experiment will be, or was. In some cases we can predict it with certainty. In others, we cannot. It is in the latter case that the calculus of probability is important. But even in this case we know something or at least we suppose that we know something. We know what the possible outcomes are. Of course, there is only one actual outcome of any experiment; but there are many possible outcomes when the result is not certain.
After the award of his Ph.D., Chuaqui returned to Chile and was appointed to the Department of Mathematics in the Faculty of Sciences of the University of Chile. He was visiting professor at the University of California, Los Angeles, 1967-1968, and in the following year began publishing papers. His first was Cardinal algebras and measures invariant under equivalence relations which appeared in the Transactions of the American Mathematical Society in 1969. In fact Chuaqui had begun writing this paper while still in Berkeley and had submitted it on 1 January 1965. It was revised three times before it was published, which explains the delay. The paper begins:-
There have been discussions from time to time of "abstract measures" the values of which need not be numerical. One of the purposes of this paper is to present arguments in favour of the use of cardinal algebras as values for these measures. Cardinal algebras were introduced and developed by A Tarski in 'Cardinal algebras' (1949). They have many of the good properties of real numbers and arise naturally ...
He attended the January Meeting of the American Mathematical Society in San Antonio, Texas, in 1970 and gave the paper A complete characterization of Lebesgue measure in terms of translation, reporting on a couple of results from his 1969 paper, to the Session on Logic and Foundations. His address at this time is given as Universidad Catolica de Chile and the Institute for Advanced Studies. Let us explain this change of address.

When Chuaqui took up his position in the Department of Mathematics in the University of Chile in Santiago de Chile he began enthusiastically contributing to its development. Up to the first half of the 1960s, those who wished to study mathematics in Chile had to attend the Pedagogical Institute, which trained teachers, or studied in engineering departments. The University of Chile had just established a Department of Mathematics in the Faculty of Engineering and in 1965 had begun teaching a B.Sc. degree in Mathematical Engineering. Chuaqui did not agree with other members in the Faculty of Engineering on the direction that mathematics teaching should take and in 1969 he resigned and was appointed as a professor at the Pontifical Catholic University of Chile.

Abraham Robinson had met Chuaqui when he had visited the University of California in 1967. Robinson asked Chuaqui if it would be possible to hold the first Latin American meeting of the Association for Symbolic Logic in Chile. Chuaqui was enthusiastic and a committee was set up, with Chuaqui as chairman, to organise the meeting at the University of Chile in January 1969. The Faculty at the University of Chile were unhappy with this proposal, however, and refused to allow the meeting to take place. This was one of the difficulties which led to Chuaqui resigning in 1969.

When he attended the January 1970 American Mathematics Society meeting he was based in Princeton since he was a member of the School of Mathematics at the Institute for Advanced Study from September 1969 until May 1970. Returning to the Pontifical Catholic University of Chile, he was appointed dean of the newly created Faculty of Exact Sciences and began setting up a Graduate Programme in Exact Sciences. Unlike the University of Chile, the rector Fernando Castillo Velasco and other leading members of the Pontifical Catholic University, were enthusiastic about holding the First Latin American Symposium on Mathematical Logic and it took place in July 1970 with Chuaqui as chairman of the organising committee. The Symposium consisted of three weeks of short courses, a Seminar with three courses and one week of invited lectures and contributed papers. Symposia continued to be held every two or three years with the nineteenth Symposium taking place in San José, Costa Rica in July 2022.

Chuaqui published many papers over the following years beginning with: Cardinal algebras of functions and integration (1971); A representation theorem for linearly ordered cardinal algebras (1971); and Forcing for the impredicative theory of classes (1972). The paper [17] lists 49 research papers, 2 research books, 3 textbooks, 3 long reviews and 16 other papers by Chuaqui. This list is also reproduced in [2].

In 1973 there was a military coup in Chile that ended the government of President Salvador Allende. A military junta, supported by the United States President Richard Nixon, took over, ended all political activity and repressed all left-wing movements. By 1974 Augusto Pinochet became president and ruled until 1990. In the difficult years of 1974-75 Alfred Tarski visited Chuaqui [11]:-
The Pinochet regime had been in power for just a year when Tarski visited in 1974-75. A military coup had ousted the duly elected president Salvador Allende, who had been attempting to implement a socialist programme. Following the coup, Allende disappeared; it was officially stated that he had committed suicide but widely believed that he had been murdered. As a consequence of these events, many people fled the country in fear or dismay. Chuaqui himself had been criticised by some of his colleagues for remaining in Chile. So the very fact that Tarski had come at that time made all the Chilean academics who were still there - carrying on as best they could - grateful to him, because many foreigners had refused invitations and had tried to discourage others from accepting. As a matter of principle, Tarski rarely refused his presence or his recommendation based upon political differences. The notable exceptions were due to egregious anti-Semitic behaviour. Recreational travel, as one would expect, was an important part of Tarski's stay in Chile. Guided by the Chuaqui family, including their three young children, Alfred and Maria toured many of the high points of the country both in the north and the south - not to climb but at least to view the mountains and do some easy hikes. They drove to the coast and there, on Valentine's Day, Tarski was invited to tea at the home of Eduardo Frei Montalva, the president who had preceded Allende. Tarski felt much honoured by that invitation.
Chuaqui, himself, made many research visits, for example: the University of São Paulo in 1971 and 1982; the University of California at Berkeley in 1973-74; Campinas State University in São Paulo in 1976, 1977 and 1978; Stanford University funded by a Guggenheim Scholarship in 1984; and San José State University in California during 1986-89. He was Dean of the Faculty of Mathematics of the Pontifical Catholic University of Chile in 1982-1983 and had a second term as Dean beginning in 1990.

In 1981 Chuaqui published the book Axiomatic set theory. Impredicative theories of classes and ten years later in 1991 he published a second book Truth, possibility and probability. New logical foundations of probability and statistical inference. You can read extracts from the Prefaces and from reviews of these books at THIS LINK.

To understand a little of Chuaqui's character, we quote from Renato Lewin [16]:-
Rolando Chuaqui did not stand out only as a scientist and manager of national mathematical development, he was also a man of great human qualities. His fruitful work in so many fields could be carried out thanks to an extraordinary capacity for work. He used to spend hours in front of his computer writing either mathematics papers, reports or class notes. The way to rest for him was simply to change the subject. Aware of the leading role he had to play in the academic environment, he was able to overcome his timid nature to convince the authorities of the importance of science in the development of the country and put into practice the numerous projects in which he participated. He was an extremely kind and simple person. His door was always open to receive anyone who needed to speak to him, from the most important authority, to the novice student and the most modest official. Deeply Catholic, his faith was not based on his great intellectual capacity nor on his doctrinal knowledge, but on an almost naive conviction. For him, this was a Truth that needed no justification.
Chuaqui received many honours for his contributions. He was elected a Full Member of the Chilean Academy of Sciences in 1977 and became its Vice President since 1991. He was elected a Corresponding Member of the Academy of Sciences of the State of São Paulo in 1982, a Full Member of the Academy of Sciences of Latin America in 1983 and a Corresponding Member of the Argentine Academy of Exact and Natural Sciences in 1988. He was a member of the Mathematical Society of Chile and served three terms as its President, the last in 1993-94.

Since 1999 the Universidad de Santiago de Chile, the Pontificia Universidad Católica de Chile, the Universidad de Valparaíso, the Universidad de Chile and the Universidad de Concepción have held an annual conference named the 'Rolando Chuaqui Kettlun Conference in Philosophy and Sciences'. The 22nd such conference was held in October 2022 at the University of Chile. Chuaqui had also been honoured by the Pontificia Universidad Católica de Chile with the building which houses the Department of Mathematics named for him.

Let us end with a quote from the interview [10] that Chuaqui gave in 1982. He was asked what characteristics a Bachelor's programme in mathematics should have. He replied:-
The Bachelor's programme must provide basic training in the main branches of mathematics, whether it is a specialisation in an area of immediate application, or an in-depth study that allows the student to continue their training as a researcher. In any case, the programme must be made up of a reduced number of core courses, in such a way that no more than four courses per semester can be followed. This is due in part to the greater importance of mathematical maturity over the extent of knowledge.

References (show)

  1. A I Arruda, N C A da Costa and R Chuaqui (eds.), Non-Classical Logics, Model Theory and Computability (North-Holland Publishing Company, Amsterdam - New York - Oxford, 1977).
  2. Catálogo de Obras de Rolando Chuaqui, Rolando Chuaqui Kettlun Conferences.
  3. R B Chuaqui M.D., A definition of probability based on equal likelihood, Ph.D. Thesis (University of California, Berkeley, 1965).
  4. N C A da Costa, Review: Axiomatic set theory. Impredicative theories of classes, by Rolando Basim Chuaqui, Studia Logica: An International Journal for Symbolic Logic 45 (3) (1986), 329-330.
  5. N C A da Costa O Bueno and S French, The Logic of Pragmatic Truth: In Memory of Rolando Chuaqui, Journal of Philosophical Logic 27 (6) (1998), 603-620.
  6. L P de Alcantara, Review: Axiomatic set theory. Impredicative theories of classes, by Rolando Basim Chuaqui, Mathematical Reviews MR0629105 (83e:04003).
  7. C A di Prisco, J A Larson, J Bagaria and A R D Mathias (eds.), Set Theory. Techniques and Applications (Springer Science Business Media, 1998).
  8. F R Drake, Review: Axiomatic set theory. Impredicative theories of classes, by Rolando Basim Chuaqui, The Journal of Symbolic Logic 49 (4) (1984), 1422.
  9. Editorial Revista Proyecciones, Rolando Chuaqui Kettlun, Proyecciones 13 (1) (1994), 1-2.
  10. L Editores, Entrevista al Dr Rolando Chuaqui K, Proyecciones 1 (1) (1982), 15-19.
  11. A B Feferman and S Feferman, Alfred Tarski. Life and Logic (Cambridge University Press, 2004).
  12. C Gutiérrez and F Gutiérrez, Carlos Grandjot, tres décadas de matemáticas en Chile: 1930-1960, Boletín de la Asociación Matemática Venezolana 11 (1) (2004), 55-84.
  13. B C Jahiatt, Rolando Chuaqui en la Escuela de Medicina, Rolando Chuaqui Kettlun Conferences.
  14. Jornadas Rolando Chuaqui Kettlun, Rolando Chuaqui Kettlun Conferences.
  15. H E Kyburg Jr, Review: Truth, possibility and probability. New logical foundations of probability and statistical inference, by Rolando Chuaqui, Mathematical Reviews MR1159708 (93h:03021).
  16. R Lewin, Vida y Obra - Rolando Chuaqui Kettlun, Rolando Chuaqui Kettlun Conferences.
  17. Obituary: Rolando Chuaqui Kettlun (1935-1994), Journal of the Chilean Mathematical Society (1994), iv-xvi.
  18. W Quezada and R Lewin, Semblanza Académica de Rolando Chuaqui Kettlun, Rolando Chuaqui Kettlun Conferences.
  19. E D Rojas and F Oteiza, Chile: The Context and Pedagogy of Mathematics Teaching and Learning, in Bruce R Vogeli, Hector Rosario and Patrick Scott (eds.), Mathematics And Its Teaching In The Southern Americas: With An Introduction By Ubiratan D'ambrosio (World Scientific Publishing Co, 2014), 89-114.

Additional Resources (show)

Other pages about Rolando Chuaqui:

  1. Rolando Chuaqui's books
  2. The Pedagogical Institute of Chile

Other websites about Rolando Chuaqui:

  1. MathSciNet Author profile
  2. zbMATH entry

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update November 2022