The war began with an uprising in July 1936 which was essentially a military plot. The uprising failed but then it developed a more religious aspect with the Nationalists taking the role of the church against secularists. But it also had aspects of a class war of industrialists and bankers against urban workers and of centralists against liberal regionalists. Where did Alberto Dou stand in all this? He was a deeply religious man and his Church was certainly encouraging its followers to join the Nationalist cause led by the Fascist Francisco Franco. However, Dou was from Catalonia which was the centre of the Republican cause. At the outbreak of the Civil War, Dou joined the Nationalist army and was sent to the front, first as a Private and later promoted to Alférez Provisional Ⓣ. He played a part in the Nationalist campaign that attacked the Republican forces at Aragon in March 1938. The Nationalists fairly quickly defeated the Republicans and took control of parts of Catalonia. It appears that following this, Dou was involved in a dispute with some fellow soldiers in his unit on whether Catalan is or is not a true language. When the captain heard that his men had been carrying out this argument, he lined up the men and challenged anyone who defended Catalan to take a step forward. Dou took that step forward and as a consequence he spent the rest of the war in a disciplinary battalion.
After the Civil War ended in 1939, Dou returned to Madrid and continued his studies in civil engineering at the Polytechnic University of Madrid. However, he also began taking mathematics classes but every morning before classes began he would attend mass at the convent of the Trinitarian Fathers. He was awarded a degree in Civil Engineering in 1943 and, for his outstanding work, he was awarded the Manuel Becerra Extraordinary Prize. In the same year he entered the Jesuits, the Society of Jesus. Already he was studying mathematics and he worked towards a philosophy degree from the Faculty of the Society of Jesus in Sarriá and a mathematics degree from the University of Barcelona. For his philosophy degree he wrote a dissertation, Probability, Statistics and Truth, supervised by Ramón Puigrefagut, based on the work of Richard von Mises. He was awarded a philosophy degree in 1949 and a bachelor's degree in mathematics in the following year. He was awarded the Extraordinary Prize for his work in mathematics.
At the University of Barcelona, Dou attended a course delivered by Wilhelm Blaschke who was visiting the university. As a result of this, immediately following the award of his bachelor's degree in mathematics, Dou went to Germany and spent a year at the University of Hamburg undertaking research supervised by Blaschke. This research involved investigating the application of differential geometry to differential equations. Returning to Spain, he defended his thesis Cuatritejidos planos Ⓣ at the Universidad Complutense of Madrid in 1952 and published his work as Quatritejidos planos Ⓣ in the Memorias de la Academia de Ciencias de Barcelona in 1953. Remarkably, in parallel with these studies in mathematics, he began studying for a doctorate in theology at the University of Innsbruck in 1951-52, and completed his research at San Cugat del Vallés in 1955. Before this, in 1954, he had been ordained a priest in the Society of Jesus. In 1955 he was appointed to the Chair of Mathematics at the School of Engineering in Madrid, and in 1957 he won the Chair of Mathematical Analysis III (Differential Equations) at the Universidad Complutense of Madrid. He found that the duties he had made it difficult to undertake research so he decided to adopt a strategy. He said (see ):-
The preparation of classes, the attention to students, the administrative tasks, absorbed so much of my time that it was virtually impossible to do any research. It occurred to me that the solution to finding some quiet time during which to study was to request periodically, every four or five years, a one-year leave of absence and to spend it in university centres abroad.He established contacts with many of the leading mathematicians such as Fritz John, Alberto Calderón and Jacques-Louis Lions. In 1959-60 he made a research visit to the Courant Institute of the University of New York and, in the same year, took the opportunity to visit the University of Chicago where he established a close relation with Antoni Zygmund and Alberto Calderón. He spent the academic year 1963-64 at the Mathematics Research Center of the University of Wisconsin in Madison where he worked with Rudolf Langer (1894-1968). In 1969-70 he visited the University of Notre Dame in Indiana, while in 1974 he returned to the Courant Institute to spend a semester there.
Dou's main areas of research were Differential Geometry, the Theory of Elasticity, and the Variational Theory of Partial Differential Equations. For example, early in his career he published Rang der ebenen 4-Gewebe Ⓣ in the Journal of the Mathematical Seminar of the University of Hamburg (1955), La representación simétrica de los cuatritejidos hexagonales Ⓣ (1957), El principio de Saint-Venant en las vigas Ⓣ (1961), Beam with a ring for cross-section, excited by longitudinal and body forces in the Proceedings of the International Conference 'Partial Differential Equations and Continuum Mechanics' held at the University of Wisconsin in Madison (1961), El teorema de unicidad en elasticidad plana Ⓣ (1962), and Sistemas diferenciales ordinarios lineales con coeficientes constantes Ⓣ (1962). Also in 1962 he published obituaries of Wilhelm Blaschke and of Julio Rey Pastor.
We should look briefly at some of the books which Dou wrote. In 1964 he published Ecuaciones diferenciales ordinarias. Problema de Cauchy Ⓣ. It was reviewed by Donald Greenspan:-
In order to achieve a degree of unity, to be relatively comprehensive, and to have a reasonable length, this new text directs attention only to the Cauchy problem for a single equation and for systems of equations. The content is divided into four main divisions which deal with methods of solution; existence, uniqueness and continuation of solutions; systems of linear equations; and numerical methods. ... the author's material is vital and well-organized; his presentation is beautifully balanced with informality and rigour; and his style is fluid and fluent. Within the reasonable scope that he has set, the author has written an excellent text.Ecuaciones en derivadas parciales Ⓣ was published in 1968 and, two years later, in 1970 Dou published Fundamentos de la matemática Ⓣ. This introductory book, written at an elementary level, has the following chapters:
Introduction. Part I: The historical development of the mathematical method. Chapter 1, The Greek period; Chapter 2, From J Saccheri to B Riemann; Chapter 3, The arithmetization of analysis. Part II: Analysis of the mathematical method. Chapter 1, Logicism; Chapter 2, Formalism; Chapter 3, Formal theory of numbers; Chapter 4, Intuitionism.His next book was Ecuaciones en derivadas parciales de primer orden e introducción a las de segundo orden Ⓣ (1970) which had the following contents:
Chapter I: First order partial differential equations. (A) Semilinear equations: (1) Introduction, (2) Integral surfaces and first integrals, (3) The Cauchy problem; (B) The general equation with two independent variables: (4) Monge curves, (5) The Cauchy problem, (6) The method of the complete integral, (7) The example p2 + q2 + f(x, y) = 0; (C) The equation with more than two independent variables: (8) The Cauchy method, (9) The Hamilton-Jacobi method. Chapter II: Introduction to second order equations. Typical examples from applied mathematics: (1) The membrane equation, (2) The heat equation, (3) Equations of elliptic type.In 1972 he published a text in English, namely Lectures on partial differential equations of first order. Wolfgang Haack writes:-
This book is the result of lectures which the author gave at the Universities of Madrid and Notre Dame (Indiana), and represents the first part of a planned "Introduction to the theory of partial differential equations''. Thus, the part under review is completely introductory in nature.In collaboration with Alfredo Mendizabal he wrote Ecuaciones en derivadas parciales y su resolucion numerica Ⓣ which was published in 1973.
Let us now describe briefly how Dou's career developed. He held the Chair of Mathematical Analysis III (Differential Equations) at the Universidad Complutense of Madrid (UCM) from 1957 and, in 1967 he was appointed director UCM's new Department of Functional Equations in the Mathematics Section of the Faculty of Sciences. In 1975 he was elected as Dean of the new Faculty of Mathematics at UCM. However, he was to hold this post for only a short time since he accepted the position of rector of the University of Deusto in San Sebastián. This university, the oldest private university in Spain, was run by the Society of Jesus and so was a natural for Dou to accept this position. He related an interesting event that happened when he presided over the opening ceremony of the 1976-77 session :-
For me the most enriching experience that occurred came when I was the Rector of the University of Deusto and presiding over the opening ceremony of the 1976-77 session. When the Secretary finished reading the Report for the academic year 1975-76, a group of law students came to the presidential dais on their own initiative and tried to read the written counter-memorial they carried with them. A noisy commotion immediately broke out. I stood up, asked for silence, and authorised them to read their counter-memorial. When the reading was over, it seemed that they were going to leave, but I indicated to them that they should remain and listen to us since we had listened to them; and they stayed.However, Dou only remained at the University of Deusto for two years before, in 1977, he returned to Madrid when he accepted the position as rector of the Catholic Institute of Arts and Industries and of the Catholic Institute of Business Administration. These institutes were run by the Society of Jesus and had merged in 1960. In 1978, one year after Dou took up this position, these institutes merged with the Comillas Pontifical University which was also run by the Society of Jesus. When he had come back to Madrid from San Sebastián in 1977 Dou also returned to his Chair of Mathematical Analysis III (Differential Equations) at the UCM.
In addition to his research in Differential Geometry, Differential Equations, and the Theory of Elasticity, Dou wrote articles on the foundations of mathematics. For example El infinito en matemáticas Ⓣ (1968), El teorema de incomplitud de Gödel Ⓣ (1969), and Fundamentos de la Matemática Ⓣ (1970). He wrote about artificial intelligence in articles such as Implicaciones de la inteligencia artificial para el conocimiento humano Ⓣ (1972) and about the history of mathematics in articles such as Logical and historical remarks on Saccheri's gometry (1970), Las matemáticas de Galileo. Estudio histórico sobre Ⓣ (1986), and Euclides (1986). He also wrote about the meaning and impact of science and technology on society in articles such as Aspectos Moral y Social de la investigación Ⓣ (1965), Humanismo en el año 2000 Ⓣ (1973), Un sacerdote en la Universidad Ⓣ (1974), and El sentido de la técnica Ⓣ (1984).
His interest in the history of mathematics is clearly seen from the fact that after he retired from his positions in Madrid in 1983 he went to the University of Barcelona where he was given the position of Professor Emeritus, teaching the History and Philosophy of Mathematics. He published many articles on the history of science while in that position. For example, Orígenes del cálculo de Variaciones Ⓣ (1988), Mathematics in Spain in the 17th century (1989), Orígenes de la geometría no Euclidiana: Saccheri, Lambert y Taurinus Ⓣ (1992), The emergence of the consciousness of the possibility of a new non-Euclidean geometry (1993), Matemáticos españoles jesuitas de los siglos 16 y 17 Ⓣ (1997), Las Teorías del movimiento de los proyectiles y de las paralelas de Aristóteles a Einstein Ⓣ (1999), Influencias negativas de la cultura y en particular de la filosofía en la emergencia de la primera geometría no Euclídea Ⓣ (2000). He also wrote many articles on science and theology, for example El científico cristiano, la humanidad y la Iglesia Ⓣ (1988), A propos de la théologie du sens: Le langage sur Dieu Ⓣ (1992), Els científics i la fe cristiana Ⓣ (1993), and Scientists and the Reformulation of Gospel Message (1996).
Dou received many awards and honours for his outstanding contributions. In 1960 he was elected President of the Royal Spanish Mathematical Society succeeding Julio Rey Pastor. On 12 June 1963, Dou delivered his inauguration address as a member of the Royal Spanish Academy of Exact, Physical and Natural Sciences occupying the place left vacant on the death of Rey Pastor. In 1974 he received the Civil Order of Alfonso X the Wise for his qualities as a teacher. In 1989 he received the Gold Medal of the College of Civil Engineers, and finally Honorary Doctorates from the Universidad Pontificia de Comillas in 1984 and from the University of Málaga in 2002.
Dou said the following about his own career :-
The teacher who passionately gives a university course, whether or not he is aware of it, also imparts a vision of the cosmos and of life, and students, whether they want it or not, whether they know it or not, are critically impacted by the course, either towards an acceptance or to a rejection of human values or pseudo-values, independently of the mathematical contents or of the discipline that is taught. Personally, for me, after living for a while in a kind of schizophrenia between religious values and mathematical values, I soon came to the conclusion that they converged on a single humanism. I have sometimes summed it up in one sentence: From the pulpit to the dais there is no continuous solution.Let us end with some quote from his friends and colleagues ( and ):-
He never concealed his prevailing Jesuit status, he lived in the way of the Jesuits without ostentation, but without complexes, without dramatic tears or false steps. He was able to be faithful to his time and his destiny with a simplicity that was always exemplary.
Seldom have I seen so much human simplicity in a scientific personality with such deep values.
He gave his life passionately to the University and always made his knowledge a genuinely university service.
With his death, Spanish science and culture suffer the loss of a privileged and wonderfully open mind that, impregnating a ubiquitous footprint in many fields, will always endure in the memory of all those who were offered his teaching, collaboration and friendship. Rest in peace.
Article by: J J O'Connor and E F Robertson